On the Dynamics of a Fractional-Order Ebola Epidemic Model with Nonlinear Incidence Rates

Mirirai Chinyoka,Steady Mushayabasa,Tinashe B Gashirai,Yuriy Rogovchenko

doi:10.1155/2021/2125061

Abstract

We propose a new fractional-order model to investigate the transmission and spread of Ebola virus disease. The proposed model incorporates relevant biological factors that characterize Ebola transmission during an outbreak. In particular, we have assumed that susceptible individuals are capable of contracting the infection from a deceased Ebola patient due to traditional beliefs and customs practiced in many African countries where frequent outbreaks of the disease are recorded. We conducted both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction number. Model parameters were estimated based on the 2014-2015 Ebola outbreak in Sierra Leone. In addition, numerical simulation results are presented to demonstrate the analytical findings.

Highlights

In recent decades, fractional calculus theory has been applied in many fields such as mechanical and mechanics, viscoelasticity, bioengineering, finance, optimal theory, optical and thermal system, and electromagnetic field theory [1,2,3]
We propose a fractional-order modeling framework for Ebola virus disease (EVD) that incorporates nonlinear incidence rates
Recent studies have shown that fractional-order differential equations are more ideal to model many real-world problems in engineering, biology, chemistry, and so on since fractional derivatives are dependent on historical states in addition to the current state and they possess memory properties

Summary

Introduction

Fractional calculus theory has been applied in many fields such as mechanical and mechanics, viscoelasticity, bioengineering, finance, optimal theory, optical and thermal system, and electromagnetic field theory [1,2,3]. There is growing interest among researchers to study the role of fractional calculus on modeling real-world problems. One field that has attracted a lot of interest in the application of fractional calculus is mathematical modeling of infectious diseases [2, 3]. A fractional-order Ebola epidemic model that incorporates nonlinear incidence rates is proposed and analyzed. A plethora of mathematical models have been proposed to explain, predict as well as quantify the effectiveness of different Ebola virus disease (EVD) intervention strategies since the 2004 when the largest outbreak occurred in Africa (see, for example, [5,6,7,8,9,10,11,12,13,14], and references therein)

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