Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

Md Abdul Kuddus,Azizur Rahman,M Mohiuddin

doi:10.1038/s41598-021-95913-8

Abstract

Although the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one (mathrm{i}.mathrm{e}. , , {mathrm{R}}_{0}<1). This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one (mathrm{i}.mathrm{e}. , , {mathrm{ R}}_{0}<1), and if greater than one (mathrm{i}.mathrm{e}. , , {mathrm{R}}_{0}>1) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on {mathrm{R}}_{0}. The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute {mathrm{R}}_{0} and measles prevalence left({mathrm{I}}^{*}right) with respect to the estimated and fitted model parameters. We found that the transmission rate (upbeta ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

Highlights

We developed a compartmental transmission dynamics measles model between the following mutually exclusive compartments: susceptible individuals, S(t) ; those who have not yet infected with the disease but might become infected; first dose vaccinated individuals, V1(t) ; those who have received the first dose of vaccine; second dose vaccinated individuals, V2(t) ; those who have received the second dose of vaccine; Exposed individuals, E(t) ; representing those that are infected and have not yet developed active measles disease; Infected individuals, I(t) ; those who are infected and infectious; and Recovered individuals, R(t) ; those who were previously infected and successfully recovered
Two types of equilibrium solutions appear in this system: the disease-free equilibrium, which is reached when the basic reproduction number is less than one, i.e. R0 < 1 and the endemic equilibrium, which is reached when the basic reproduction number is greater than one, i.e. R0 > 1
This paper has developed and analyzed a compartmental transmission dynamics measles model with double dose vaccination in Bangladesh

Summary

Introduction

OPEN Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination To examining the stability of the equilibria of system (9)–(13), the following outcomes are proven: Lemma 1 The disease-free equilibrium of the model is locally asymptotically stable if R0 < 1 and unstable if R0 > 1. We perform the sensitivity of the model basic reproduction number (R0) and measles prevalence (I∗) to the model parameters using the Latin Hypercube Sampling (LHS) method with 10,000 runs per simulation.

Results

Conclusion