Machine Learning Approach for the Prediction of COVID-19 Spread in Nigeria Using SIR Model

The outbreak of the COVID-19 virus took the world by surprise at the start of 2020 and has had a serious impact on businesses, economies, healthcare and human life in general. The virus was initially named “2019-nCoV” and then renamed to “SARS-CoV-2” due to its similarity to the SARS-CoV [1]. Mankind has always suffered from the aftermath of epidemics that have always plagued the world dating back to the accounts recorded in the evolution of man. The famous plague called the Black Death was said to have wiped out about half the population of Europe. The plague was around for over 300 years and caused frequent outbreaks causing the death of almost 200 million people [2]. The Spanish flu in 1918 was the first pandemic, which occurred during the setting of modern medicine, and it had a death toll of over 50 million people. Severe Acute Respiratory Syndrome (SARS) occurred in the 21st century and was caused by the SARS coronavirus. It had a death toll of fewer than 10,000 but had a mortality rate of 10%, and this raised a serious concern. It was contained by the middle of 2003.

In December 2013, the Ebola virus appeared in a village in Guinea and spread to most countries in Central and West Africa, with over 28,000 cases and 11,000 deaths [2]. There are other notable epidemics that have plagued the world over time, such as the Circa of 3000 B.C., the plagues of Athens, the Justinian Plague, the Antonine plague, the great plague of London in the 17^th century, The H1N1 Swine Flu, the AIDS- Acquired Immuno-Deficiency Syndrome pandemic which started in 1981 and has lasted till present day; the Zika virus and the Lassa fever pandemic [3]. Following the emergence of COVID-19 in Nigeria, several measures were put in place to curb the spread of the virus.

Operations of domestic and international flights came to a halt, all schools were immediately closed, while only essential workers were permitted to be physically present at work, all other workers were to work remotely and the wearing of nose masks in public places was enforced. The NCDC- National Centre for Disease Control set up various testing centres across the country and presented live updates concerning the number of tests carried out, confirmed cases, recovered cases, and fatalities. With the frequent occurrence of these epidemics, it has become very important to study, track and predict the spread of these diseases using statistical and mathematical models [4, 5].

One of the major assumptions of the classic SIR model is that there is a homogeneous mixing of the infected and susceptible populations and that the total population is constant in time. In the classic SIR model, the susceptible population decreases monotonically towards zero [6].

1.1 COVID 19 and Nigeria

Nigeria is the most populated nation in Africa with over 200 million people, out of which over 6.5 million people are over the age of 65 years [7]. These individuals aged 65 and above are the ones at risk of suffering more in this pandemic. Alas, Nigeria does not have the expected volume of standard healthcare system that can cater for its citizens during a pandemic of this magnitude. It also lacks the resources to carry out accurate contact tracing which can lead to the number of reported cases being lower. All 36 states in Nigeria including the FCT have reported cases of COVID 19 and the spread is reflected in Figure 1.

1.png

Figure 1. A map showing the spread of COVID 19 across Nigeria [8]

Lagos, Oyo, and FCT were the states with the highest number of cases while Cross River and Kogi states had the least number of cases. The case Fatality Ratio is 2% and the gender distribution shows that the infected persons are 65% male and 35% female. The gender distribution for infected cases are as reflected in Figure 2.

2.png

Figure 2. Gender distribution for infected cases [8]

The COVID-19 pandemic caused Nigeria to come to a standstill for three months in the year 2020 with the closure of schools and businesses; there seems to be no adequate plan for sustainability because there was not enough information on the pandemic to plan for the future. Studying data collected during this pandemic will aid in predicting the future and putting plans in place.

The choice of Nigeria in context is largely based on its infrastructural deficits, literacy rate, skyrocketing poverty rate, unemployment, and global poor economic status when the population is considered. There was so much fear globally that that the above-stated parameter would completely crumble Nigeria since those factors make ignorance inclined, and a contagious disease like COVID-19 was to bring the country to extinction. It is therefore paramount that this paper has addressed the factors and conditions that finally kept the pandemics’ fatality in check and revealing predictions based on machine learning which finally correlates with the reality on ground based on the spread, peak, and the stopping time of the pandemic.

Furthermore, the predictive analysis was a necessity in Nigeria because the existing health facilities, interconnection of medical services, and pandemic management system was almost at point zero when the pandemic struck. It was therefore essential to swiftly employ machine learning prediction techniques to gain future insights in Nigeria or face extinction if there was no clear cut way forward. As a quick fix was in place, updating the medical system and test samples handling system, personnel training, importation of vaccines and others this work’s prediction helps to determine the volume of resources needed per time based on the knowledge of the peak and a stop of the pandemic, which was correct in real life. The prediction avoided wastage of resources or having less health utilities while the pandemic peaks. The insights as given by the work saved lives and resources as it launched Nigeria into its unknown world where a remedy must be provided on time.

The COVID 19 disease affects the respiratory system and the causative agent is the SARS-CoV-2. Pneumonia appears to be the most serious manifestation of infection. The symptoms associated with this disease are fever, sore throat, cough, dyspnoea, headache, rhinorrhoea, nausea and diarrhoea [9]. The period from the emergence of COVID-19 symptoms to demise ranges from 1 to 5 weeks, with a 2-week average. This time depends mainly on the status of the patient's immune system and the patient's age. Patients over the age of 65 and patients with underlying health issues are at risk of the virus having a greater effect.

1.2 Forecasting techniques

Forecasting involves the estimation or prediction of future events. There are various techniques used in forecasting and they are categorized into the following four groups.

Big Data: Analysis of big datasets is done by using mathematical equations and machine learning techniques. The accuracy of the forecast is highly dependent on the data sources used for forecasting.

Mathematical Models: Mathematical and Stochastic theory has been applied during the past few pandemics to predict death count and has proven to be very effective.

Data Science/Machine Learning Techniques: The accuracy of machine learning techniques makes it the most used technique worldwide for forecasting. There are various machine learning models which can be used in forecasting, it is necessary that the right model is always used depending on the analysis.

1.3 Predictive analytics

Predictive analytics is a field of data analytics which makes use of present and past information to predict what will happen in the future.

The different models used in predictive analytics are: predictive, descriptive, and decision models. Predictive analytics involves various steps in the process of forecasting, these steps are represented in Figure 3.

3.png

Figure 3. Predictive analytics process [10]

1.4 Predictive analytics techniques

(i) Time Series Analysis: This is a method which utilizes data gathered across a period of time at intervals to forecast the future.

(ii) Decision Tree: A classification model that relates decision to possible outcomes. Its operations are as shown in Figure 4. With basic groupings into branches to solve problems further.

4.png

Figure 4. Decision tree [10]

(iii) Regression Model: This is a popular predictive technique that models relationships between dependent and independent variables.

(iv) Artificial Neural Networks: This is a sophisticated model based on a network of artificial neurons with the ability to process input signals and produce output. This is depicted in Figure 5.

5.png

Figure 5. ANN layers [11]

1.5 Time series forecasting

Time series forecasting involves predicting the future after careful analysis of past data. Time series forecasting is commonly used in predicting stock market prices, exchange rates and natural occurrences [12]. Auto-Regressive Integrated Moving Average (ARIMA), TBAT, Deep R and N-Beats are a few methods used in time series forecasting [13].

1.6 Exploratory data analysis (EDA)

Exploratory Data Analysis is the process of analyzing data sets to gain insights on their characteristics using visual methods. Exploratory Data Analysis is basically checking for what can be learned from the data beyond the formal modelling. The graphical techniques used in EDA are: Odds ratio, Box plot, Scatter plot, Histogram, Parallel coordinates, Run chart, Pareto chart, Multidimensional scaling, Multilinear PCA, Ordination.

Time series forecasting is a technique for predicting future events by analyzing past trends, based on the assumption that future trends will hold similar to historical trends. Forecasting involves using models fit on historical data to predict future values, which provides a data-driven approach to effective and efficient planning. This is as found in the COVID-19 scenario and makes the time series forecasting a choice approach in this research.

Furthermore, exploratory data analysis as employed in this work helps determine how best to manipulate data sources to get the answers you need, making it easier for data scientists to discover patterns, spot anomalies, test a hypothesis, or check assumptions. COVID-19 being a pandemic new in its existence as featured in this research has to depend on a powerful tool for pattern discovery as found in the employed exploratory data analysis. There are several goals of exploratory data analysis, which are: To determine if there are any problems with your dataset; to determine whether the question you are asking can be answered by the data that you have or not, and these are crucial to a pandemic prediction context of this work.

The SIR model is more suitable to predict the epidemic trend due to the spread of the disease as it can accommodate surges and be adjusted to the recorded data. By comparing the published data with predictions, it is possible to predict the success of government interventions [6].

In order to carry out this research, raw data on COVID-19 pandemic in Nigeria was gotten from John Hopkins University https://github.com/CSSEGISandData/COVID-19. The data was analysed using Python packages in Google Colab. The SIR - Susceptible, Infected, Recovered or Removed population model which is a model used for modelling epidemics was employed to predict the spread of the pandemic in Nigeria.

3.1 Data collection

The data used to carry out this study was collected from live links on GitHub, provided by the John Hopkins University (JHU). There were 4 datasets collected for this study, (i) the dataset that consists of daily COVID-19 confirmed cases, (ii) the dataset that consists of daily COVID-19 recovered cases, (iii) the dataset that consists of daily COVID-19 fatalities and (iv) the dataset that consists of cases by countries. These datasets are stochastic in nature; they consist of time series data starting from 1/22/2020 and are updated daily.

3.2 Data cleaning

In this stage, irrelevant fields were eradicated from the dataset. Only the fields that were necessary to the study were retained. This is done before analysis to make the model more accurate. Figure 6 below details the data cleaning cycle, while Table 1 shows relevant fields in the dataset.

6.png

Figure 6. Data cleaning cycle [21]

Table 1. Relevant fields in the datasets

3.3 Data analysis

For the analysis of this research, the following packages that are necessary for the analysis were imported as discussed below:

Pandas: This is a library written for python language and it can be used for data analysis and manipulation. It has operations and data structures that are adequate for manipulating time series data. Dataframes in pandas can be used to download data in csv format which was used in this study. The pandas data structures are shown in Table 2.

Table 2. Pandas data structures

NumPy: It is a python library with multi-dimensional arrays and matrix data formats which can be used to execute mathematical and logical operations.

SciPy: It is a package that expands NumPy 's functionality with a large set of important algorithms such as regression, Fourier transformation, minimization and other mathematical techniques [22].

3.4 Data visualization

In this study, Plotly was used for visualization purposes. Plotly is an interactive, open-source graphing library for python. Plotly was chosen because it provides a feature that no other visualization library has-interactivity: This allows users to interact with graphs on display, allowing for a better storytelling experience. Zooming in and out, point value display, panning graphs, you name it, they have it. Plotly displays data in an extra ordinary version while seaborn and matplotlib are for basic plotting.

Plotly was used to visualize the data in this study, showing the confirmed COVID 19 cases globally in Figure 7, case trend for COVID 19 globally in Figure 8; while Figure 9 reveals Nigeria's COVID 19 case trend.

7.png

Figure 7. Confirmed cases globally

8.png

Figure 8. Global COVID 19 case trend

9.png

Figure 9. Nigeria's COVID 19 case trend

3.5 SIR- susceptible, infected, recovered or removed population model

The SIR model is used to describe basic principles of a pandemic. In this model, the total population is divided up into three categories:

(i) S – Susceptible population;

(ii) I – Infected population;

(iii) R - Recovered/removed population.

The susceptible population are people who can potentially contact the virus, the Infected are those who currently have the virus and can transmit the virus to others, and the Recovered/Removed are those who have contacted the disease and have either been cured or have succumbed to the effects of the virus.

The variables in this model are: S, I, R, R_0, β, γ with each meaning expressed in (1-6) and the stages represented in Figure 10.

S - The number of susceptible people.

I - The number of infected persons.

R - The number of persons that have recovered.

R₀- Basic Reproduction ratio which characterizes how the pandemic will grow.

Β - The transmission coefficient.

γ - The recovery coefficient.

10.png

Figure 10. SIR –susceptible, infected, recovered or removed population model

Though Melikechi et al. [23] outlined some limits of epidemic prediction using SIR. The SIR model can be used to model some of the possible scenarios if the early relaxation of restrictions leads to increasing number of susceptible populations. If there is a relatively small increase in the future number of susceptible individuals, no series impacts occur.

3.5.1 Differential equations

This model is given by three equations:

Eq. (1): Rate of change of susceptible population

$\frac{d S}{d t}=-\beta \mathrm{IS}$                    (1)

where, I=the number of infected; S=the number of susceptible population.

Eq. (2): Rate of change of infected

$\frac{d I}{d t}=\beta \mathrm{IS}-\gamma \mathrm{I}$                          (2)

where, γ=the constant rate of change of removals.

Eq. (3): Rate of change of recovered/removed

$\frac{d R}{d t}=\gamma \mathrm{I}$                   (3)

Knowing the total number of the susceptible population, S, the total number of infected population, I, and the total number of recovered or removed population, R, is constant. Therefore, we have: $\frac{d(S+I+R)}{d t}$=0 and it is also know that the total population is made up of the susceptibles, the infected and the removed and this is also constant, so S+I+R=S₀+I₀. This is constant by our first assumption. Therefore, the model is termed a closed model for this reason. At first, we have everybody susceptible and the quantity of recovered or removed is zero. As time advances the number of susceptible declines as people get contaminated. Individuals move from the S class into the I class.

As the amount of susceptible reduces and the amount of recovered or removed increases, the contaminated people increases yet levels out and afterward begins to decline. So $\frac{d I}{d t}>0$ when time t=0 and the epidemic begins. The transition between a pandemic and a non-pandemic spread of a disease occurs when $\frac{d I}{d t}=0$ and this occurs when $\mathrm{S}_0=\frac{\gamma}{\beta}$. Also, the peak of a pandemic occurs when $\mathrm{S}=\frac{\gamma}{\beta}$. and the rate of change of the infected group stops growing and starts reducing. Therefore, we can flatten the curve. Figure 11 shows an SIR model solution example.

11.png

Figure 11. Example of an SIR model solution [24]

The variety, volume, and velocity of data as presented in Tables 3, 4 and 5 concerning the pandemic may not be handled by statistical approach alone, hence; the choice of machine learning for this work. To the best of our knowledge, no previous work on COVID-19 prior 2020, except for the general epidemiology and breakout of other diseases in the past. However, subsequent happenings after the breakout of the novel pandemic have corroborated the predictions made by this work, most especially the peak period as proved by earlier presented graphs which are products of the developed model in this work.

This work serves as one of the reference works in pandemic prediction in the African context with the choice of datasets from Nigeria except for comparison as given by centre for disease control in chosen continents. The peculiarity of weather and friendliness or otherwise of the virus to heat in Africa calls for more collaboration research in Virology and machine learning to curb the limitations of required dataset availability.

The model provided in this work aids decision making ahead of time possible. Predictions are correctly made into the future and the government can adequately prepare for expected government actions to tackle a disease, knowing the peak period and the time it disappears provided the necessary vaccines are taken and medical advice are heeded.