Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method

Emmanuel A Bakare,Radovan Potucek,Snehashish Chakraverty

doi:10.3390/axioms10020114

Abstract

This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). The SIR epidemic model is proposed and solved under different uncertain intervals by the HAM to obtain the numerical solution of the model. Furthermore, the SIR ODE model was transformed into a stochastic differential equation (SDE) model and the results of the stochastic and deterministic models were compared using numerical simulations. The results obtained were compared with the numerical solution and found to be in good agreement. Finally, various simulations were done to discuss the solution.

Highlights

Interval analysis is a method developed by mathematicians in the 1950s as a way of handling bounds or rounding errors and measurement errors in mathematical computation
We have developed the stochastic version of the SIR epidemic model presented in this paper in order to measure the effect of randomness of the variables in the model
We present the results of the homotopy analysis method for solving an interval-based uncertain model

Summary

Introduction

Interval analysis is a method developed by mathematicians in the 1950s as a way of handling bounds or rounding errors and measurement errors in mathematical computation It is useful in formulating numerical methods that yield desirable results. This work aims to formulate interval arithmetic that solves upper and lower endpoints for the range of values of a particular function in one or more variables. Considering the classical calculation with real numbers, simple arithmetic operations and functions on elementary intervals must initially be defined. It is after this that complicated functions can be evaluated from the basic elements. We state the range of possible outcomes explicitly

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Results

Conclusion