Using Mathematical Modeling to Predict the Spread of

Epidemics

Nabaa Fawze1,*

1 Ministry of Education–Wasit Directorate of Education, Iraq

Email: fawzenaba@gmail.com

Received: October 18, 2025 Revised: December 12, 2025 Accepted: January 19, 2026 ⋆ Corresponding author

ABSTRACT

In this paper, we give a brief overview of the advances in mathematical modelling applied to epidemiology and the

achievements that have been made in epidemiological research using mathematical models. Since the early 1900s

when the well-known susceptible–infected–recovered model was proposed, mathematical treatments have played an

important role in epidemiology. We introduce the deterministic SIR model and explain the value of computational

tools, mathematical modelling and statistical analysis for the understanding of the development of disease and the

size of emerging outbreaks. These are issues that are of major concern in everyday life and public health. With the

emergence of the novel coronavirus in recent times, it has become evident that mathematical modeling along with

computational and statistical tools are extremely relevant. Hence, this study explains the mathematical modelling in

Epidemiology and demonstrates the advancement of the discipline over the years.

Keywords: Epidemic Mathematical modeling Influenza SIR model Disease spread

1. INTRODUCTION

Everyone is concerned about health and health is one of the

main issues that is dominating the media these days all over

the world. The COVID-19 pandemic is one such epidemic

outbreak that had affected numerous countries and made this

worry evident. Besides, new types of harmful chemicals

in the environment have been found and it is necessary to

intervene and take effective steps to reduce their effects.

Epidemic is a disease which spreads rapidly among a population.

It has been a threat to the life of human beings,

societies and even national economies throughout history.

There is therefore a need to adopt a variety of strategies to

control and contain the spread of epidemics. Mathematical

modelling in epidemiology provides a way for scientists to

develop principles and rules that can explain and predict the

dynamics of disease and how it may spread in the future.

Through mathematical models, epidemiological equations

and computational simulations, researchers can simulate the

spread of disease and formulate suitable solutions and strategies

for implementing informed decisions about public health

worldwide [1, 2, 3].

2. ADVANCES IN MATHEMATICAL MODELLING

Mathematical modelling has played an important role in enhancing

infectious-disease management in underserved regions.

However, heavy reliance on deterministic models

reduces the flexibility needed to address changing epidemiological

conditions. Furthermore, limitations in data accuracy

and availability negatively affect the robustness of modeling

results. Future research should therefore emphasize the development

of more diverse modelling frameworks, improvement

of data-collection systems, and inclusion of a wider spectrum

of infectious diseases. These outcomes may contribute to

public-health policy by enabling evidence-based decisionmaking,

optimizing resource distribution, and strengthening

the incorporation of modelling techniques into epidemic