Modeling the Spread of Malaria Using SIR Epidemic Model in Ibadan

Abstract

Malaria remains one of the most persistent public health challenges in sub-Saharan Africa, especially in Nigeria, where climatic and environmental conditions favor the breeding of mosquitoes. This study focuses on modeling the spread of malaria in Ibadan using the Susceptible–Infected–Recovered (SIR) epidemic model. The model divides the population into three interacting compartments—susceptible, infected, and recovered individuals—to describe disease transmission dynamics over time. Differential equations were used to estimate infection and recovery rates, and the model parameters were fitted using available epidemiological data from the Oyo State Ministry of Health. Time-series simulations revealed the critical threshold (basic reproduction number, R0R_0R0​) that determines whether malaria will persist or die out in the population. The results aim to assist policymakers and health organizations in designing effective intervention strategies such as improved sanitation, mosquito control, and increased public health education.

CHAPTER ONE: INTRODUCTION

1.1 Background to the Study

Malaria is one of the most severe parasitic diseases affecting humans, especially in tropical regions. It is caused by Plasmodium parasites transmitted through the bites of infected Anopheles mosquitoes. According to the World Health Organization (WHO), Nigeria contributes a significant portion of global malaria cases and deaths annually. Ibadan, the largest city in West Africa by land area, experiences a high incidence of malaria due to its warm climate, poor drainage systems, and dense population.

Mathematical modeling plays a crucial role in understanding the spread and control of infectious diseases. The SIR epidemic model is one of the fundamental models used to describe how diseases spread within a population. By dividing individuals into compartments — Susceptible (S), Infected (I), and Recovered (R) — researchers can analyze transmission rates, recovery rates, and disease persistence. The model provides insights into how interventions such as vaccination, vector control, and awareness campaigns can influence disease outcomes.

Modeling malaria transmission in Ibadan using the SIR framework helps to quantify infection dynamics, forecast future cases, and evaluate the effectiveness of prevention strategies.

1.2 Statement of the Problem

Despite continuous health campaigns and malaria control programs, the rate of malaria infection in Ibadan remains high. Several factors contribute to this persistence, including environmental conditions favorable to mosquito breeding, insufficient use of treated nets, and limited access to healthcare services.

Existing studies often describe malaria prevalence without applying mathematical frameworks to predict its spread or the effects of intervention measures. There is, therefore, a need to use SIR mathematical modeling to represent malaria transmission and evaluate possible control measures quantitatively.

1.3 Aim and Objectives of the Study

The main aim of this study is to model the spread of malaria in Ibadan using the SIR epidemic model.

The specific objectives are to:

1. Develop a mathematical model describing malaria transmission using the SIR framework.

2. Estimate key parameters such as infection rate, recovery rate, and basic reproduction number (R0R_0R0​).

3. Analyze the stability of the disease-free and endemic equilibria of the model.

4. Simulate the model using available data from Ibadan to study infection dynamics.

5. Recommend control strategies to minimize malaria transmission in the study area.

1.4 Research Questions

1. How can the SIR model describe the transmission dynamics of malaria in Ibadan?

2. What are the estimated values of infection and recovery rates for malaria in the area?

3. What is the threshold condition (R0R_0R0​) for malaria persistence or eradication?

4. How can the results of the model inform malaria prevention and control policies?

1.5 Significance of the Study

This research is significant because it combines mathematical modeling and epidemiological data to understand malaria transmission. The findings will:

• Provide a scientific basis for predicting malaria trends in Ibadan.

• Help public health officials identify the most effective intervention points.

• Contribute to the academic field of mathematical epidemiology by applying the SIR model to a real-life problem.

• Support evidence-based policymaking aimed at malaria eradication.

Moreover, understanding the spread pattern can guide resource allocation for insecticide-treated nets, mosquito control programs, and medical supplies.

1.6 Scope of the Study

The study focuses on Ibadan Metropolis, Oyo State, Nigeria. Data on malaria infection and recovery will be obtained from hospitals, public health records, and environmental surveys within the city. The analysis is restricted to the SIR model, and the population is assumed to be closed, with births and natural deaths neglected during the study period. The research will cover a time frame of five years (2020–2024).

1.7 Limitations of the Study

The study’s limitations include incomplete or inconsistent malaria reporting from some healthcare centers, environmental factors not directly captured in the model (such as rainfall or temperature), and the simplifying assumptions of the SIR model (e.g., homogeneous mixing of individuals). Despite these constraints, the model still provides valuable insights into malaria transmission dynamics.

1.8 Definition of Terms

• Susceptible (S): Individuals who are healthy but can contract malaria.

• Infected (I): Individuals currently infected with the malaria parasite.

• Recovered (R): Individuals who have recovered and acquired temporary or partial immunity.

• Basic Reproduction Number (R0R_0R0​): The expected number of secondary infections produced by a single infected person in a wholly susceptible population.

• Transmission Rate ($\beta$): The rate at which susceptible individuals contract the disease from infected individuals.

• Recovery Rate ($\gamma$): The rate at which infected individuals recover and move into the recovered class.