# Analysis of SIR Epidemic Model with Different Basic Reproduction Numbers and Validation with HIV and TSWV Data

• Mausumi Dhar
• Paritosh Bhattacharya
Research Paper
Part of the following topical collections:
1. Mathematics

## Abstract

In this paper, the SIR epidemic model containing three classes of individuals in a closed population: susceptible, infected and recovered is considered. The nonnegativity and boundedness of solutions of the model equations are entrenched and how the basic reproduction number determines the severity of an epidemic outbreak is analyzed. The general reproduction number is determined, and the role of general reproduction number in predicting the nature of epidemic progress is illustrated. An analytical solution of the model has been developed by using Picard’s method as well as the obtained solution has been compared to the numerical solution derived by the Monte Carlo simulation method. To validate the analytical solution, the system of solutions has been fitted to clinical global data provided by WHO and some experimental data taken from the literature and has been shown that despite of some significant errors, the analytical solution yields approximated result as per the clinical as well as experimental data.

## Keywords

SIR epidemic model Reproduction numbers Analytical solution Validation Human Immunodeficiency Virus (HIV) Tomato Spotted Wilt Virus (TSWV)

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