### Analysis of Basic Reproduction Number in Epidemiological Model

#### Manaye Chanie 1* , Demeke Fisseha 2

1 Department of Mathematics, Jinka University, Jinka, Ethiopia

2 Department of Mathematics, Debre Markos University, Debre Marqos, Ethiopia

#### Received: 3 October 2020; Accepted: 4 March 2021; Published: 6 April 2021

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### Abstract

In this project we present analysis of basic reproduction number in epidemiological model. Epidemiological analysis and mathematical models are now essential tools in understanding the dynamics of infectious diseases and in designing public health strategies. The threshold for many epidemiological models is the basic reproduction number R_0. It reflects the average number of secondary infections produced by one infected individual put into completely susceptible host society. It is a threshold quantity which determines whether the epidemic will occur or not. We will discuss the general SIS, SIR and SEIR model with vital dynamics for the mathematical modeling of diseases. The reproduction number and the stabilities of both the disease-free and the endemic equilibrium will be calculated. Finally numerical simulations using Matlab Software will be conducted for SIR model with vital dynamics.

### Keywords

Mathematical Model, Reproduction Number, Deterministic (SIS/SIR/SEIR) Model, Disease-Free Equilibrium, Endemic Equilibrium, Simulation

### Copyright

© 2017 by the authors. Licensee International Technology and Science Press Limited. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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