Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Modelling and Stability Analysis of the Dynamics of Measles with Application to Ethiopian Data

Hailay Weldegiorgis Berhe
* ORCID logo ,
Habtu Alemayehu Atsbha
,
Yohannes Yirga Kefela
,
Abadi Abraha Asgedom
,
Abadi GMeskel
,
Woldegebriel Assefa Woldegerima
ORCID logo ,
Shaibu Osman
,
Lamin Kabareh
Version 1 : Received: 22 March 2023 / Approved: 23 March 2023 / Online: 23 March 2023 (06:11:58 CET)

How to cite: Berhe, H.W.; Atsbha, H.A.; Kefela, Y.Y.; Asgedom, A.A.; GMeskel, A.; Woldegerima, W.A.; Osman, S.; Kabareh, L. Modelling and Stability Analysis of the Dynamics of Measles with Application to Ethiopian Data. Preprints 2023, 2023030410. https://doi.org/10.20944/preprints202303.0410.v1 Berhe, H.W.; Atsbha, H.A.; Kefela, Y.Y.; Asgedom, A.A.; GMeskel, A.; Woldegerima, W.A.; Osman, S.; Kabareh, L. Modelling and Stability Analysis of the Dynamics of Measles with Application to Ethiopian Data. Preprints 2023, 2023030410. https://doi.org/10.20944/preprints202303.0410.v1

Abstract

Measles is a highly contagious airborne disease that is endemic in many developing countries with low levels of vaccination coverage. In this paper, we propose a deterministic compartmental mathematical model for measles disease dynamics. We establish the global stability conditions for the disease-free and endemic equilibria using the Lyapunov function stability method. \textcolor{red}{Using arbitrary parameters it is obtained that the proposed model exhibits forward bifurcation}. Numerical integration using MATLAB software was used to simulate the model solution of the forward problem. We calibrate the proposed model to estimate the parameters with a 95\% confidence interval (CI) using real data from Ethiopia by formulating an inverse problem. We notice that the model fits well with the real data of Ethiopia. The estimated basic reproduction number ($R_0$) is found to be $R_0=1.3973$ which proves that the disease is endemic. It is also obtained from the local sensitivity analysis that reducing the transmission rate and increasing the vaccination rate could effectively minimize the $R_0$.

Keywords

measles; basic reproduction number; global stability; vaccination; forward bifurcation; model calibration

Subject

Medicine and Pharmacology, Medicine and Pharmacology

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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