A Predictive Mathematical Model
EXECUTIVE REPORT
May 3, 2020
By Yusuf Yau Gambo
Applied Mathematician and Data Analyst Yusuf Maitama Sule University, Kano
Yunus A. Abdulhameed, PhD
Biomedical Physicist Yusuf Maitama Sule University, Kano
Reviewed by:
Professor (Emeritus) Peter McClintock
Expert in Biomedical Physics, Nonlinear Dynamics
and Low Temperature Physics Lancaster University, UK
Professor Basant Kumar Jha Expert in Mathematical Modelling Ahmadu Bello University, Zaria, Nigeria
yygambo@nwu.edu.ng yygambo@gmail.com yunusabhamid@gmail.com
+234 810 404 4144
As leaders across the country begin to think about how to re-open the economy, our model Predictive Mathematical Modelling based on ordinary differential equations projects that coronavirus cases in Lagos and Kano would skyrocket if the states suddenly returns to normalcy.
Our team from Yusuf Maitama Sule University Kano in collaboration with our counterparts abroad, using NCDC data, projected about 2,038 and 1,444 total cases of the virus in Lagos and Kano with a peak coming in mid-June and early June respectively. But those figures rely on the states keeping the current restrictions in place.
With just a 50 percent increase in mobility – people leaving their homes, shopping, going to work and socializing – the model projects that number would leap to 102,600 and 645,500 in Lagos and Kano states, respectively. Meaning, if measures are relaxed by 50 percent in these states, our model projects that the number would skyrocket to these figures.
Lifting restrictions entirely would bring 868,700 and 919,900 total cases in Lagos and Kano respectively.
With the evidence that we have, (the virus) cannot be stopped at the moment. We’ve to alter our traditional, cultural and even religious and social norms, the way we operate, the way we work, until there is a vaccine or cure.
On a final note, we have the best model; the agreement between the model and the data is nearly perfect. Moreover, a colleague who is currently at Lancaster University, UK, alongside his colleagues have tested and fitted the model with COVID-19 data received from 20 most populated cities in USA.
Our hope is that, these predictions will provide the authorities concerned with an insight on the potential dynamics behind the transmission of COVID-19 in the two most populated states in Nigeria.
This report is intended for the general public, and therefore we summarize the main findings and leave aside the mathematical details.
Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. The first cases of COVID-19 disease surfaced in late December 2019 in Wuhan city, the capital of Hubei province in China. The disease is causing devastating public health impact across the world. On January 30, 2020 The World Health Organization (WHO) declared the virus as a public health emergency of international scope and subsequently declared it to be a global pandemic. As of April 30, 2020, COVID-19 has spread to over 210 countries and territories, causing over 3 million infections and 217,769 deaths. Moreover, as at April 30, 2020, Nigeria has recorded a total number of 1,932 confirmed cases of COVID-19 with 58 deaths spreading across 34 states and the FCT. Lagos state was the first state in Nigeria reported to have one case of COVID-19 on February 27, 2020 but Kano did not have early presence of the pathogen until 11th April, 2020. An early response prevented an escalation in the number of cases in Kano state. Had the state government not acted early by giving a lockdown order, a significant rate of infection would have been inevitable. Currently, the lockdown in both Lagos and Kano states has slowed down the progression of the disease, although the partial lifting of the lockdown from time to time in the states could also result in more rise in number of new cases. The lockdown allows the health system to prepare for what is likely to be an inevitable surge. Initially, there was no clarity about the impact of asymptomatic carriers in the dynamics of the disease globally. Knowledge about this matter is still evolving. However, it has become increasingly evident that COVID-19 is a highly infectious pathogen that behaves in ways very different to many other respiratory diseases. The SARS-CoV-2 virus is a highly infectious, relentless pathogen. Once the state lockdown is lifted, a surge in cases is to be expected shortly after. Optimal control will be needed to minimize contagion for several months, until a vaccine is widely available to the public.
The dynamical model for the spread of COVID-19 is formulated by decomposing the total host population (N) into the following five epidemiological classes: susceptible human (S), exposed human (E), symptomatic human (Y), asymptomatic human (A), and recovered human (R).
In every epidemic, some individuals become sick and some may die, whereas others recover from illness and still others show no signs or symptoms of disease, while
nonetheless carrying it and being potential sources of infection. A susceptible human is a person who is at risk of becoming infected by a disease. An exposed human is a person whose body host an infection but is not yet able to transmit the disease. A symptomatic human on the other hand is an individual that shows symptoms after becoming infected. An asymptomatic human is a carrier for a disease or infection but experiences no symptoms. Lastly, a recovered individual is a person that has recovered from a disease.
Figure 1: Schematic diagram of a COVID-19 model including an asymptomatic compartment. The arrows, except the disease-induced death (?), represent progression from one compartment to the next. Hosts progress through each compartment subject to the rates described below.
A colleague and his collaborators tested the model first on the 20 most populated cities in the United States of America and it fitted very well with their factual data. The model predicts the possible number of cases that may arise when the current state of lockdown in Lagos and Kano States is lifted. In this report, there is a good agreement between data obtained from Nigeria Center for Disease Control (NCDC) and the mathematical model.
Figure 2: Transmission Scenarios for the Current and 20% Mobility in Lagos State.
Figure 3: Transmission Scenarios for the 50% and Normal Mobility in Lagos State
Figure 4: Transmission Scenarios for the Current and 20% Mobility in Kano State
Figure 5: Transmission Scenarios for the 50% and Normal Mobility in Kano State
Cumulative (or total) cases refer to the combined cases of the symptomatic, asymptomatic, recovered and death cases. The active cases are those cases of people that show symptoms.
Changes in behavioral patterns in response to an outbreak have an effect on the propagation of a disease. As people gain awareness of the presence of an infectious disease in their communities, a portion will take measures in order to reduce their susceptibility. An example of this behavior corresponding to the COVID-19 pandemic is that of social distancing. Indeed, the cancellation of events likely to attract crowds, the closing of schools, and working from home will have a drastic impact on the size of the susceptible population at any given time. From Figures 2-5, mathematical analysis reveals the following insights:
It is important to note that without testing for the virus on a massive scale, only less number of cases could be confirmed while a good percentage of people carrying the infection would remain undetected.
Based on the above figures, we conclude that without strict adherence to social distancing, coronavirus cases in Lagos and Kano would rise steeply as our model projects huge number of cases in the two states without continued enforcement of social distancing. Therefore should governments deem it necessary to re-open the economy, we recommend the following:
I. Only partial mobility should be allowable.
II. Any person over the age of 10 and is in a public space within Lagos and Kano States should now be required to wear a face mask.
III. Employers should be required to provide face coverings for employees and government should provide the face masks for citizens that cannot afford.
IV. Restaurants and bars should be ordered to close dining areas but may maintain take-out, drive-thru and curbside pickup options.
V. Higher institutions should be conducting lectures online if possible, else no lecture room should be occupied by more than 40 people.
VI. Faculties, departments and other places in higher institutions should be required to place large hand sanitizer dispensers at every entrances and exits.
VII. Worship centers should remain closed until after each state had reach peak of the wave, then the places of worship could be reopened. However, even after attaining the peak, there is also a potential likelihood of another resurgence (second phase) of the virus. But as data continues to emerge, we shall properly be able to provide more predictions.
1. WHO, Coronavirus (Accessed on April 22, 2020).
2. WHO, Coronavirus disease (COVID-2019) situation reports (Last accessed on April 30, 2020).
3. WHO, Director-General’s opening remarks at the media briefing on COVID-19 – 11 March 2020.
4. Nigeria Centre for Disease Control (NCDC), COVID-19 Situation Reports (Last accessed on April 30, 2020).
5. E. Dong, H. Du, L. Gardner (2020). An interactive web-based dashboard to track COVID-19 in real time, The Lancet Infectious Diseases.
6. Calistus et al. (2020). Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus, arXiv:2004.07391v1 [q-bio.PE] 15 Apr 2020.
