Using mathematics to understand and control the 2019 novel coronavirus pandemic

BY ABBA B. GUMEL

The world is currently facing a devastating pandemic of a novel coronavirus (COVID-19), which started as an outbreak of pneumonia of unknown cause in the Wuhan city of China in December of 2019. Within days and weeks, the COVID-19 pandemic has spread to over 210 countries. By the end of April 2020, COVID-19 has caused over 3 million confirmed cases and 230,000 fatalities globally. China was the original epicenter of COVID-19, followed by Italy and now the United States (with the state of New York shouldering the overwhelming brunt of the COVID-19 burden). As of April 29, 2020, the US has recorded over 1 million confirmed cases and 61,000 deaths. The first documented confirmed case of COVID-19 in the US was reported on January 20, 2020. This was linked to a resident who has returned from a trip to Wuhan city. Although it was possible that COVID-19 was already spreading in the state of New York by mid-February 2020, the first index case was documented in New York state on March 1, 2020. This was traced to a woman who traveled to New York city from Iran (a country that was ravaged by COVID-19 at that time).

I gave the dates for the index cases in New York state and the entire US to illustrate an important point, namely the exponential nature of the spread of the COVID-19 pandemic during the early stages of its outbreak. Starting with the single case on March 1, 2020, the state of New York recorded nearly 70,000 by the end of March 2020 (with about 1000 deaths). Further, the number of confirmed cases skyrocketed to over 300,000 by the end of April 2020 (and 17,000 deaths). These numbers clearly illustrate the exponential spread of the pandemic! We will come back to this later. Most of the COVID-19 related deaths and severe cases occur in the elderly (65 years of age and older) and people with co-morbidities (such as people with diabetes, hypertension, obesity, kidney disease and other conditions that suppress or compromise the immune system, such as people living with HIV/AIDS). Younger people and frontline healthcare workers are also at high risk of acquiring COVID-19 infection. This article introduces some of the basic principles associated with the use of mathematics to understand the transmission dynamics and control of infectious diseases, such as COVID-19, in human populations.

What are coronaviruses, you might ask.   Coronaviruses (CoV) represent a major group of RNA viruses that cause diseases in mammals and birds. Human coronaviruses (HCoV) represent a major group of coronaviruses associated with multiple respiratory diseases of varying severity, including common cold, pneumonia and bronchiolitis. While the mild form of coronavirus infections causes diseases such as the common cold, the lethal form can cause diseases like the severe acute respiratory syndrome (SARS-CoV), middle eastern respiratory syndrome (MERS) and COVID-19 (caused by SARS-CoV-2). The name “coronavirus” is derived from the Latin word “Corona” for crown or wreath. It signifies “the characteristic appearance of the virions (the infective form of the virus), which have a fringe of large, bulbous surface projections creating an image reminiscent of the solar corona or halo”. In other words, “coronaviruses” are the crown-jewel of all viruses here on earth.

Zoonotic scientists estimate that there are millions of viruses in the wild, and humans are always vulnerable to mutations in these zoonotic viruses that could trigger pandemics. HCoVs, rated among the most rapidly evolving viruses due their genetic makeup (notably due to their high genomic nucleotide substitution rates and recombination), have their origins in bats and rodents. Data shows that the evolution of HCoVs has been expedited in recent years due to urbanization and poultry farming (resulting in the frequent mixing of species and facilitating the crossing of species barrier and genomic recombination of these viruses).

Six known human coronaviruses have been identified in recent years. These include the 2002/2003 pandemic of severe acute respiratory syndrome (SARS-CoV), a highly transmissible disease which started in the Guandong province in China and spread to 29 countries (causing 8,000 cases and 744 fatalities globally), and the 2012 pandemic of the middle eastern respiratory syndrome (MERS-CoV), which started out of Saudi Arabia and spread to 27 countries (causing 2,519 cases and 866 deaths by January 2020). Over 80% of MERS-CoV occurred in Saudi Arabia. Palm civet and bats were implicated as the natural reservoirs of SARS-CoV (which has a mortality rate of 10%). MERS-CoV, which was believed to have likely originated from bats, and then likely spread from infected dromedary camels to humans, has a mortality rate of about 35%. Both SARS-CoV and MERS-CoV have similar clinical symptoms, namely atypical pneumonia marked by fever, headache and subsequent onset of respiratory symptoms (such as cough and pneumonia), which may later develop into life-threatening respiratory failure and acute respiratory distress syndrome.

As was the case with the two other coronaviruses (SARS-CoV and MERS-CoV), COVID-19 (SARS-CoV-2) is transmitted from human-to-human through direct contact with contaminated objects or surfaces and through inhalation of respiratory droplets from both symptomatic and asymptomatically-infectious humans. There is also limited evidence that the virus can be exhaled through normal breathing. The incubation period of the disease ranges from 2-14 days, and most infections (over 80%) show mild or no clinical symptoms of the disease. The common symptoms include fever, coughing and shortness of breath for mild cases, and pneumonia for severe cases. There is currently no safe and effective vaccine for use in humans (although some promising candidate vaccines are undergoing various accelerated stages of clinical trials in humans). There are also no safe and approved antiviral drugs for use to treat COVID-19 patients (although there are a number being tested in humans, such as remdesivir, with potentially promising effectiveness). Hence, efforts aimed at controlling and mitigating the burden of COVID-19 are focused on the implementation of non-pharmaceutical interventions, such as social-distancing (and other measures for reducing community transmission, such as community lockdowns), using face-masks in public, quarantine of suspected cases, isolation and hospitalization of confirmed cases and contact-tracing of confirmed cases.

Since the novel 2019 coronavirus is transmitted among people who come in close contact with each other, the implementation of strict social-distancing measures has been the primary tool for curbing the spread of the pandemic. As of April 7, 2020, stringent social-distancing mechanisms (which, in addition to maintaining 6-feet physical separation with other humans, entails mandatory lockdowns/ stay-at-home orders) have been imposed in over 42 states of the United States, together with Washington DC, Guam, and Puerto Rico (representing over 95% of the US population; involving approximately 316 million Americans). In fact, the state of New York (the current epicenter for COVID-19) has even imposed a fine against people who fail to comply with its stringent social-distancing measures that took effect March 22, 2020. Common social-distancing measures or guidelines being employed in the US include temporary closures of schools and non-essential businesses, avoiding crowded events and mass gatherings, moving in-person meetings online, etc. The city of Wuhan lifted its 76-day strict lockdown on April 8, 2020 (this was done in a phased way, with the first relaxation of measures on February 9, 2020).

Now we come to the COVID-19 situation in Nigeria, the most populous country in Africa (with over 200 million citizens). The Nigerian Centre for Disease Control (NCDC) reports the first confirmed COVID-19 case in Nigeria on February 27, 2020. As of April 29, 2020, data from the website of the NCDC shows that Nigeria has recorded 1,278 confirmed cases and 51 deaths. The data showed that Lagos State currently has 718 active cases and recorded 21 deaths, and the new epicenter, Kano State, has 136 reported cases and 3 residents of the state have died of COVID-19. Even if these seemingly grossly under-reported COVID-19 case and mortality numbers are to be believed for a second, the fact that the ancient city of Kano has over 100 confirmed cases, and considering its sheer population size (of over 10 million residents) and highly dense nature, for instance, suggests a potentially catastrophic COVID-19 outcome for the city and the rest of Kano state (and, perhaps, the neighboring environs). There are two obvious reasons to substantiate my claim. The first is that Kano city is like New York city in terms of population size and population density. The second is that, in the absence of serious public health interventions (particularly strict social-distancing protocols and other measures for reducing community transmission), the pandemic is going to grow in an exponential manner, as we saw in New York city and the rest of the state of New York. The Kano State Government has finally acknowledged, on April 27, 2020, the “mysterious deaths” of over 640 inhabitants. This prompted President Buhari to order a complete lockdown of the state the following day. A very laudable move.

Kano city is a major commercial hub. In fact, it has historically been the commercial capital of the whole of West Africa. It is also the nucleus and focal point of the Nigeria’s north. It is home to all the nationalities/ethnicities within the north (and the south too). If Kano catches fire (i.e., if it is ravaged by COVID-19), so will the rest of the North….and, by extension, the rest of the Nigerian nation. Sadly, at the height of this COVID-19 pandemic, the government of Kano State, in its infinite wisdom, decided to “repatriate” Nigerian citizens (kids partaking in the almajiri system) back to their “state of origin”. First, it really is amazing how this kind of lawlessness can be tolerated in a federal system. How can any citizen (regardless of age or socio-economic status) be treated as a foreigner in his/her own country? Second, these kids that were “repatriated” from Kano city back to their “state of origin” may have been infected with COVID-19, thereby silently starting COVID-19 outbreaks in the locations they were forcibly re-located to by the lawless Kano State government. This irresponsible action of the Kano State government, while manifestly illegal, could contribute in exporting COVID-19 to other neighbouring states and communities. No state government has the right to repatriate any citizen. This is illegal, and the Nigerian (federal) government must hold the lawless KNSG accountable…. otherwise, our citizenship means next to nothing (since a state government or Governor can suspend it at will). This lawlessness cannot be tolerated. This now gives me perfect time to Segway to something a lot more pleasant. Mathematics. The science of precision.

Mathematics, being the universal language of nature/universe and the foundation of all the natural and engineering sciences, has historically being used to gain realistic insight into the transmission dynamics and control of emerging and re-emerging infectious diseases of public health interest. This dates back to the pioneering works of the likes of Sir Ronald Ross, a British surgeon and a polymath, who, in addition to elucidating the full lifecycle of the malaria parasite (Plasmodium) in birds and in humans in Freetown, Sierra Leone, in the 1890s, introduced the notion of threshold analysis in the control of infectious diseases. He showed, using a simple mathematical model involving two differential equations for the temporal dynamics of the population of infected mosquitoes and infected humans, that we do not need to kill all mosquitoes to effectively control malaria. All that was needed was to reduce the mosquito population below a certain threshold, and malaria will be effectively controlled (or even eliminated from the community). This was what was done to eliminate malaria from Western Europe. He won the 1902 Nobel Prize in Physiology or Medicine.

In the 1920s, distinguished Scottish scientists (biochemist, William O. Kermack and Lt. Col. Anderson G. McKendrick, military physician and epidemiologist) formulated the much-celebrated mathematical framework for modeling infectious diseases. Their modeling framework is based on stratifying the total human population into mutually-exclusive compartments based on infection status. The resulting mathematical models typically take the form of deterministic systems of nonlinear differential equations, involving a number of state variables (i.e., humans compartments) and model parameters. The resulting dynamic models are built based on incorporating all the key/pertinent epidemiological, ecological, immunological and demographic features of the disease, as well as making realistic assumptions on the key aspects associated with the disease transmission process (e.g., mixing patterns, distribution of waiting times in epidemiological compartments etc). That’s why the models are dynamic in nature. In other words, the transmission dynamics and control of the disease is now represented (or modelled) using a collection of mathematical equations, which typically take the form of differential equations (i.e., equations that measure the rate at which some epidemiological state variable of the model, such as the number of infected or hospitalized individuals, changes with time).

By using rigorous mathematical analysis, coupled with data analytics to parameterize the models, the models can be used to first reproduce the observed trajectory of the disease (i.e., the model can be validated by showing that it reasonably mimics the observed data, vis a vis the initial number of cases, hospitalizations and the disease-induced death) and, consequently, be used to make predictions on the likely course of the disease (i.e., we can then predict the expected number of cases, hospitalizations, ICU admissions and mortality in the near or distant future). Thus, mathematical modeling (or mathematical biology to be more precise) is inherently multi-disciplinary. It entails the coming together of various disciplines, notably mathematics, statistical data analytics, epidemiology, ecology, immunology, public health, computation and even the social sciences (including disciplines such as communications and behavioral analysis…. needed to determine effective ways to communicate the disease control strategies obtained from modeling to the general public).

In the context of COVID-19, for instance, a basic Kermack-Mckendrick-type mathematical model will entail subdividing the total population at time t, denoted by N(t), into the mutually-exclusive compartments of susceptible individuals (S(t); these are individuals who do not yet have the disease, but could get infected if they come in contact with someone who is already infected), exposed (E(t); these are individuals who are newly-infected but are not yet infectious. Which means they are generally not sick, and not able to pass the disease to others), symptomatically-infectious (I(t); these are individuals with the clinical symptoms of COVID-19), asymptomatically-infectious (A(t); these are infectious individuals who show mild or no symptoms of the disease), self-isolated or hospitalized (H(t)), ICU patients (Q(t)) and recovered (R(t)) individuals. This means the total population (N(t)) is given by the equation:

N(t)= S(t)+E(t)+I(t)+A(t)+H(t)+Q(t)+R(t).

A system of nonlinear differential equations is then derived for the rate of change of each of the seven state variables of the model (S, E, I, A, H, Q and R). We then rigorously analyze the temporal dynamics of the resulting model (using mathematical theories and techniques from various branches of mathematics, such as analysis, nonlinear dynamical systems, topology, graph theory, probability theory, linear algebra etc.) We essentially analyse the asymptotic dynamics of the various steady-state solutions of the model (i.e., we seek to determine conditions for the existence of such solutions, and then determine under what conditions can they attract solution trajectories). This process can be summarized in two main concepts: asymptotic stability analysis and bifurcation theory. Having completed these analyses (which are critical in determining conditions, in parameter space, needed to effectively control or eliminate the disease), we then use tools from statistics and probability theory to realistically estimate the parameters of the model (such as least square fitting and general inverse problem type approaches). Mathematical models for disease spread in human populations, such as the one briefly described above, typically have many parameters, and uncertainties may arise in estimating the numerical values of some of the parameters. For instance, during the early stages of the COVID-19 pandemic, the parameter associated with contacts between individuals may not be known precisely (i.e., we may not know, at the early stages, how many contacts, on average, each member of the community makes with other members of the community, and whether or not these contacts would lead to infection. Further, we may not even know the incubation period or recovery rate during the early stages). To account for this, we carry out detailed uncertainty analysis (using statistical techniques, such as the Monte-Carlo-based Latin Hypercube sampling technique). We can also determine which of the many parameters of the model greatly influence the disease dynamics (this will then be targeted for control strategies).   This is called sensitivity analysis, and we use tools like partial rank correlation coefficient method to rank all the parameters in terms of how important they are in determining the dynamics/trajectory of the disease with respect to the chosen response function. We also use tools from optimization theory to assess the population-level effectiveness of various proposed public health interventions. This will allow the determination of optimal ways to allocate the resources for public health interventions during disease outbreaks (such as the COVID-19 pandemic) that will result in the effective control of the disease (measured in terms of reduction in the disease burden, such as reduction in number of cases, hospitalizations, ICU admissions and disease-related mortality). In other words, mathematical modeling and analysis allow for the determination of optimal cost-effective strategies (for using the available public health resources) to achieve optimal population-level results, vis a vis the control of the disease.

A crucial mathematical quantity of major public health interest is the basic reproduction number of the model (denoted by R_0). This is the most important number public health practitioners, tasked with the control of an emerging disease or pandemic, wish to know as soon as possible. This number measures the average number of new cases of the disease generated by a typical infected individual (not an atypical one, like a super-spreader) if introduced into a completely susceptible population (i.e., a population, like ours, where no one has seen the novel Coronavirus before…..or no one has been vaccinated; hence, no one has any prior immunity against the disease) before he/she get cured or dies of the disease. For instance, R_0 = 2 implies that, on average, one infected individual will infect two others, and these two will infect four others etc. Hence, before you know it, lots of people (in thousands or hundreds of thousand or even millions) will get infected. Mathematically-speaking, this number is computed by using concepts in linear algebra to calculate the largest eigenvalue (i.e., spectral radius in linear algebra jargon) of some matrix. The early estimate for R_0 for COVID-19 was between 2 and 3. That’s why public health agencies around the world were in a heightened state of panic once mathematical modelers around the world (including our group) published their estimates for R_0 shortly after the pandemic was announced by the World Health Organization on December 31, 2019. The reason is simply that if the R_0 value for any country or community is greater than one, then that country or community will suffer a major outbreak (and the disease may become endemic). In this case, the disease will be spreading at an exploding (exponential) pace. Thousands of new cases can be generated within a few days (like we saw in New York state during March 2020). However, once intervention and mitigation measures (such as social-distancing, use of face masks in public, quarantine and isolation etc.) are implemented, the value of R_0 will begin to decrease, depending on the effectiveness and the coverage level (i.e., compliance) of the intervention measures being implemented. If it decreases to a value below unity, then the disease can be fully controlled (or eliminated), otherwise, the disease will persist in the community.

Having laid the mathematical foundation above, we can now explore why COVID-19 is far more transmissible and virulent than its two cousins, SARS-CoV and MERS-CoV. The first thing to note is that while the basic reproduction number (R_0) for SARS-CoV and MERS-CoV lie in the range (1.7-1.9) and (0.4-0.9), respectively, that of COVID-19 range between 2 and 3 (as stated earlier). Thus, on average, a person infected with COVID-19 can transmit the infection to at least two others during the duration of his/her infectiousness (i.e., before he/she recovers or dies from COVID-19). This, plus the fact that, unlike in the case of SARS-CoV and MERS-CoV, asymptomatic transmission is a dominant feature of the COVID-19 transmission dynamics, explains why COVID-19 is a lot more transmissible and fatal than its two cousins. This explains why, unlike SARS-CoV and MERS-CoV which were geographically limited in their spread (limited to only 29 countries), COVID-19 spread to every country on earth within days or few weeks. Further, this explains why the burden of COVID-19 is a lot higher (causing over 3 million confirmed cases and 230,000 deaths from December 2019 to April 2020) than the burdens of SARS-CoV and MERS-CoV combined (totaling about 11,000 confirmed cases and 1,600 deaths, globally).

You must now be wondering what all this long grammar and rigorous mathematization of epidemiology mean in the context of COVID-19 dynamics in the Nigerian nation. The answer is simple. Plenty. Nigeria is blessed with a large, and dare I say ingenious, resilient and hardworking, population (of over 200 million), and majority of the populace lives in highly dense urban areas. The public health infrastructure in Nigeria is, generally, of moderate capacity and quality. It is fair to surmise that it is probably not fully equipped to handle natural disasters of the menacing scope of COVID-19. Further, there are legitimate reasons to greatly doubt the statistics on COVID-19 collected and disseminated by the NCDC. That is, the COVID-19 surveillance and mortality data published by the NCDC (for the daily or cumulative number of confirmed cases and mortality) is, at best, remarkably suspicious. The NCDC stated that the index case in Nigeria was diagnosed/confirmed on February 27, 2020. Since COVID-19 was already spreading in China by the end of 2019, it stands to reason (considering the huge volume of traffic from Nigeria to China and vice versa) that the pandemic was brought into Nigeria a lot earlier than February 27, 2020. This means that, like in the case of many other hard-hit COVID-19 countries outside China, Nigeria has been weeks, if not months, behind the exponentially-growing COVID-19 pandemic.

Recent modeling data from Northeastern University in Boston, USA, shows that New York city might have had about 11,000 COVID-19 cases before the first confirmed case in the state was announced on March 1, 2020 (the study, backed by CDC testing data at JFK International Airport, claims that COVID-19 was already circulating in the state since late January, 2020). Some of Nigeria’s largest cities, notably Kano and Lagos, are very much like New York city in terms of both population size and population density. Hence, it stands to reason that what transpired in New York city, vis a vis the burden of the COVID-19 pandemic, should be expected to transpire in these Nigerian cities. My own mathematical modeling research group has recently studied the dynamics and control of COVID-19 in the state of New York and the entire US nation. We estimated the pre-social-distancing mortality numbers for the US to be around 160,000 (our estimate falls within the range estimated by the University of Washington Institute of Health Metrics Evaluation group, whose model is being used by the US Presidential Task Force on COVID-19). Our modeling shows that, once strict social-distancing and other measures for curbing community transmission (such as the use of face-masks, contact-tracing of confirmed cases, quarantine of suspected cases, isolation of confirmed cases etc.) are implemented, and maintained until the end of the year, the cumulative mortality numbers for the US will reduce to about 60,000. We also showed that the use of face-masks in public, even if the masks are of relatively low efficacy (such as home-made cloth masks), is very useful in curtailing the pandemic, particularly if the masks-usage policy is implemented nationwide and the coverage in its usage is high (i.e., if everyone in the nation, except young children and those who cannot wear face-masks for health reasons, are encouraged to wear masks….and majority comply with such recommendation). Face masks are primarily useful in preventing susceptible people from acquiring infection after inhaling the respiratory droplets that hand in the air after infected people (not wearing masks) sneeze or cough.

So, where do we go from here? The answer is mathematics to the rescue. I offer the following 10-point mathematical recipe for effectively controlling (or eliminating) COVID-19 in Nigeria:

1. Social-distancing and nationwide community lockdown: I know this is very controversial and imposes severe strains on people. I get it. But I also know that, in the absence of a safe and effective vaccine or antiviral, our best bet is to do everything we can to limit community transmission. The fact that the overwhelming number of new COVID-19 are generated by people who do not even know they have the disease (i.e., those with mild or no symptoms), make social-distancing and community lockdowns to be the clear best option to try to limit community transmission. These measures are certainly very tough for a society like ours, whose cultural, social and traditional norms and practices are very much inter-twined with close contacts with other people (family, friends, work, social gatherings, people at places of worship and at the community at large). We are, by definition, a collection of family-oriented and highly sociable people who live in highly dense communities. Nonetheless, these are immensely desperate times, which clearly require such desperate measures and sacrifices. The government has to find ways to ease some of the sufferings people endure during lockdowns, such as injecting massive economic stimulus packages into the economy and making food and other basic/critical amenities of life available to those who may need such (as is being done pretty much in every nation on earth). We must not rush into easing the lockdowns… until we have a good handle of what is going on (and that the number of new cases and COVID-induced mortality are declining at significant rate). I know that this is somewhat draconian, particularly at this moment when more than half of the nation are observing the fasting of the Holy month of Ramadan. Again, desperate moments necessitate desperate measures. We, as a nation, must venture into the unknown. We must do things we have never done before.
2. Do not rush to re-open the country and the economy: Yes, there is undoubtedly mounting pressure to re-open the country (i.e., to lift the lockdown). We must not rush to this. We must wait until the data (i.e., science) shows that it is okay to begin to do so. Even when it is indeed okay to begin to do so, we must do things in a very responsible and careful manner. We must do a gradual lifting of the lockdown, and re-assess situations periodically (i.e., conduct widescale testing to see how well we are doing, and, if necessary, re-adjust and revert to the lockdown if necessary). Countries that rushed to lifting of the lockdown and social-distancing measures, such as Singapore, Taiwan, South Korea, Hong Kong and now Ghana, have been recording an alarming rebound of COVID-19. Our modeling studies show that if the US re-open (i.e., lift the current strict social-distancing and lockdown measures) by end of April 2020 or even end of May 2020, the country may experience a devastating second wave of COVID-19 by middle July. The point is simply that rushing to re-open the economy could lead to devastating consequences. There is certainly a lot of pressure to do so in Nigeria, considering the huge pressure from across the country and the plummeting oil prices. But we must stay the course. We must be steadfast. We must make the necessary sacrifices to avert a potentially catastrophic disaster. An important point to note is that if we re-open now, we may not start seeing the detrimental consequence of this action until at least three or four weeks later. You may wonder what I meant by this claim. Okay, let’s illustrate this by way of an example. Suppose we re-open the country today (i.e., partially or fully lift the lockdown), and suppose someone gets infected with COVID-19 today. This person will not show symptoms of the virus until, on average, at least two weeks from today. That is, the person will not feel sick until after the 2-week average intrinsic incubation period of the disease. The person may not need to go to hospital until a week after the incubation period. This means three weeks since this person got infected. The person may take up to a week in hospital before he/she dies. In other words, from getting infected today, we may not start seeing the consequence of our ill-advised action (as measured in terms of hospitalizations and mortality) until at least three weeks after the lockdown is lifted. During these three weeks window, the infected people are, of course, busy unknowingly transmitting the disease to others. So, we may not see the devastating impact of our rush to re-open until weeks later. We must learn from others and avoid repeating their mistakes. Albert Einstein defines madness to mean doing the same thing over-and-over again and expect a different outcome. We should avoid doing what the mad would do. If we reach a point where we can re-open, we must do so responsibly (and ensure that the most vulnerable…. Particularly the elderly and those with co-morbidities) are fully protected (since they suffer the brunt of the severe disease and mortality burdens). We must do things in phases and re-adjust when necessary.
3. Implement widespread testing: This is no brainer. Widespread random testing is the only way for us to realistic know the burden of the disease. It is the only way to know who are currently infected and those who have recovered from the disease (and presumably built some protective immunity against future infections). We need to make good quality point-of-care tests readily available (and free) to all citizens. We should deploy the two types of tests. The surveillance diagnostic test to detect current infections and the serology (antibody) test to detect those that have already had, and recovered from, the disease. We have the technology and expertise to extract the neutralizing antibodies in the blood plasma of COVID-19 survivors and using them to treat critically-ill COVID-19 patients (by boosting their immunity).
4. Implement effective strict containment strategy: Once a COVID-19 case is diagnosed (following testing), that case must be rapidly isolated and his/her contacts quickly traced (via effective contact-tracing) and placed in quarantine.   We must implement this with no further delay. We must recruit an army of contact tracers that can help carry out the arduous, but necessary, task of tracing contacts of confirmed COVID-19 cases. I know that the test kits (for both the antibody serology testing and the diagnostic surveillance testing) are not widely available in Nigeria at the current moment, our government simply needs to use all its international leverages to secure these tests. It is a matter of national security. The lives of our citizens are at stake. A government’s most important (and sacred) duty is to protect the lives of its citizens.
5. Use of face masks in public: The government must require that everyone going out of their home must wear a face mask. The government has a responsibility to make this a non-negotiable public health policy. This is one of those moments where the right of the community (to be protected from a deadly disease) outweigh the right of the individual not to wear a mask (except for medical reasons). The government must make the face masks readily available (and free of charge). Face masks are widely used in many parts of the world. For example, hardly would you see anyone walking in a US street nowadays without wearing a face mask. Some US airlines (such as American Airlines, Delta Airline and Frontier Airline) require all passengers to wear face masks. Further, retail stores, such as Costco, require all their customers to wear face masks. We must require everyone to wear face masks in public. Immediately. We should have implemented this policy months ago! Better late than never, though. Mr. President, please lead by example on this one. Wear mask in public. It will save countless lives. This will encourage the citizenry to do the same. Wearing masks not only saves us from acquiring others, it saves us from passing the infection to others. We are all responsible to one another. We must all discharge our social responsibility to each other, to help save lives.
6. Avoid the disastrous Swede-miology anti-COVID strategy:   Sweden was the only country on earth who decided that their best strategy against COVID-19 was to do nothing. This new form of epidemiology, which I tagged as Swede-miology, is manifestly dangerous. In other words, implement no defence whatsoever. Their reasoning is essentially that by allowing as many residents as possible to acquire COVID-19 infection (and hopefully recover), they are building the much-needed herd immunity. Herd immunity is loosely defined as a kind of indirect protection against acquisition of an infectious disease when a large proportion of the community have become immune to the disease. There are two main ways to achieve herd immunity. The first, and the safest and most efficient, is via the use of a vaccine (to immunize as many people as possible). The second, and the riskier of the two, is to let the infection run amok in the population and hope that many will recover (and develop protective immunity against future occurrence or re-infection with the disease). Building high herd immunity (typically at least 70%) is vital in curtailing the outbreak of an infectious disease, because the disease will have limited susceptible people to target. The Swedish experiment failed flat because they recorded unprecedented mortality numbers, in comparison to the neighboring Scandanavian countries that implemented the good old-fashioned (tried-and-tested) social-distancing and community lockdown protocols.
7. Stockpile remdesivir: The US Food and Drugs Administration (FDA) has approved the emergency use of remdesivir for the treatment of hospitalized COVID-19 patients. Nigeria should pull its diplomatic muscles and levers to acquire and stockpile these drugs to use to treat COVID-19 hospitalized citizens. There is all sorts of rumors and agitation to use hydroxychloroquine, even though it has not been approved for use against COVID-19, and that some (including someone in the US city in which I live) have died after using it to “treat” COVID-19 symptoms. Our NAFDAC should be in the fore-front discouraging the use of the unapproved hydroxychloroquine, while advocating for the use of the approved remdesivir. In the same vein, our home-based and diaspora-based scientists should be encouraged to work towards the development of a safe and effective anti-COVID vaccine. We have the people with the requisite expertise to do so (for instance, the Biomedical Team assembled by Nigeria’s own Joseph Igietseme, an immunologist and vaccinologist at the CDC, can be challenged to work on this).
8. Adopt a disciplined modeling-and-data-driven public health decision making process: The NCDC and other public health agencies in Nigeria need to get real. They need to collect and report data accurately. Attempting to suppress things will help no one. We cannot cheat our way out of this deadly pandemic. That’s why we are now seeing the unbelievably high COVID-induced mortality from the so-called “mysterious illness” in Kano and elsewhere in the federation. We need to be totally transparent. People who died of COVID-like illnesses must be counted as COVID-19 fatalities. Until we know precisely (or at least reasonably accurately) the incidence of the disease, and the mortality numbers, we absolutely have no way of making realistic assessment of where we are, and where we are headed, vis a vis the transmission dynamics of the disease. Our public health agencies must base their decision-making on quality data and sound modeling. Every country on planet earth is relying on serious mathematical modeling to guide their control and mitigation strategies against COVID-19. The daily briefings by the Presidential Task Force at the White House or by Governor Andrew Cuomo of the US state of New York are heavily focused on modeling projections. I learned that Nigeria’s Presidential Task Force on COVID-19 is relying on black box models developed by some folks from a London University. This is sad to hear. Nigeria is blessed with a number of talented world-class modelers, such as Dr. Daniel Okuonghae (University of Benin) and Dr. Nafiu Hussaini (Bayero University Kano). These two are, by far, the best applied mathematicians in Nigeria today, and I have no doubt they can do a lot more than whatever the London varsity is doing for Nigerians. I have helped in training and mentoring them. I know they are world-class. I know they can do the job of providing quality mathematical assessment of the current trajectory of the pandemic. The Task Force will do well by immediately engaging them. I must, however, caution that the quality of model predictions depends, in no small measure, on the quality the model is few with. If the data (case or mortality) is flawed, the model predictions will, of course, be flawed. Again, the NCDC has no choice but to collect reliable data, and then use reliable models to have a clear (and reliable) picture of the true current burden of the COVID-19 pandemic in Nigeria, and where we are headed. It is only then can we have a more realistic assessment of the control strategies.
9. Empower and protect frontline health care workers: Our frontline healthcare workers must be given all the protective gear (personal protective equipment) they need to conduct their duties safely, without subjecting them to danger. Several of our frontline health workers have reportedly acquired COVID-19 infection while attending to their patients. It stands to reason that some of them may have even died of the disease. This must be avoided. The least we can do is to help our frontline healthcare workers. They are our only line of defence against the deadly COVID-19 beast.
10. Proactive government leadership at all levels: Leaders at all governmental levels (federal, state and local) have a duty to offer quality leadership in this trying moment. They have to constantly reach out to the people. They have to show compassion, deep knowledge of the issues surrounding the epidemiology, control and mitigation strategies against the disease. They have to show total honesty, accountability and transparency when they communicate with the people. Trying to suppress or downplay the devastating nature of the pandemic will not help anyone. The true nature and burden of the pandemic will always manifest when the time … when the time is right.

In summary, COVID-19 is a devastating pandemic we have not seen since the deadly 1918/1919 H1N1 influenza pandemic. Nigeria is now feeling the wrath of this beast. We have what it takes to effectively control its deadly menace if we get our acts together. These are desperate moments, which require desperate measures. In the absence of a safe and effective vaccine or antiviral, we have no choice but to focus on implementing (and sustaining) the tried-and-tested non-pharmaceutical interventions (such as social-distancing, community lockdown, quarantine, isolation, contact tracing, widescale random testing etc.). If we do what other nations have done (and done so successfully), we indeed can minimize and mitigate the burden of the pandemic. If we can implement and maintain strict nationwide social-distancing and community lockdown (for an extended period of time), coupled with an effective implementation of the strict containment strategy (i.e., rapidly identify and isolate a confirmed case, then trace their contacts and quarantine them), and implement widescale testing, we can certainly do very well in minimizing the devastation we otherwise would absolutely record. The authorities in Wuhan locked down the city for 76 days, and it seemed to have worked in curtailing community transmission. It is time for cooler heads to prevail in Nigeria. It is time for science and basic common sense to prevail. It is time for people to be willing and able to make sacrifices for the greater good of all (i.e., to avert a catastrophe). We all in this together. We, as a nation, have been through adversities in the past. We survived them. I believe we can survive COVID-19 if we do the right things. Yes, we can. Together. In a decidedly mathematical fashion.

I should add that one of the main take-home messages from this lengthy article is the role mathematics plays in our daily life. It shows the direct application of the many mathematical concepts we learned in high schools, undergraduate and graduate schools etc. to help save lives. The mathematics courses we were all taught during our undergraduate studies (algebra, analysis, topology, linear algebra, graph theory, dynamical system, metric spaces etc.) are all very useful in helping us understand how diseases spread, and how best to combat them (in addition to their applications in many other areas of the natural and engineering sciences). Thus, everyone must take the rigorous training in mathematics extremely seriously. In this vein, it is also imperative to emphasize the urgent need to revise our mathematics curricula at all levels of the education sector to make them more modern and suited for the 21^st century. The curricula must emphasize critical-thinking, problem-solving skills, innovation, multi-disciplinarity, originality, real-life applications, team work and comprehensive training and background in all branches of mathematics. It must also encourage data analytics, computation and ability to appreciate and address challenging problems from other disciplines. Advanced nations have many things in common. The one that is a constant is their massive investment in mathematics training at all levels. They understand that there can be no development until they build, and sustain, a culture of world-class excellence in the mathematical sciences. This is the only way to build a sustainable knowledge-based economy that is rooted in excellence in science and technology.

Bibliography

[1] Steffen E. Eikenberry, Marina Mancuso, Enahoro Iboi, Tin Phan, Keenan Eikenberry, Yang Kuang, Eric Kostelich and Abba B. Gumel. To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic. Infectious Disease Modeling. 5(2020): 293-308.

[2]. Calistus N. Ngonghala, Enahoro Iboi, Steffen Eikenberry, Matthew Scotch, Chandini Raina

MacIntyre, Matthew H. Bonds and Abba B. Gumel. Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus. Mathematical Biosciences. doi: https://doi.org/10.1016/j.mbs.2020.108364. In press.

Gumel is a foundation professor of mathematics at Arizona State University, USA. He is also a fellow of both the Nigerian Academy of Science (FAS) and the African Academy of Sciences (FAAS).