Modeling the dynamics of certain emerging epidemics
No Thumbnail Available
Date
2025
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Université Badji Mokhtar Annaba
Abstract
In this study, two general nonlinear mathematical models was iscussed. The first work develops a fractional mathematical model with general incidence rate and time delay in application to COVID-19 in Algeria owing to the disease caused by new coronavirus pandemic that emerged in China in December 2019. Analytically,the well-posedness of this model is established and discussed. Using the theory of fractional order derivative, theequilibrium stability was analyzed. In order to support analytic results, numerical simulations were carried out to identify the factors that significantly affect the disease’s ability to spreadMatlab software was used for the numerical simulations. In the second work, to explore the behavior of thesolution where the incidence function is more general, a fractional Susceptible, Exposed, Infected andRecovered SEIRepidemicmodel has been presented, where the derivative is the sense of Caputo. After provingthe basic proprieties of the solution, we use the next generation matrix approach to get the value of thefundamentalreproduction number noted R . We 0 will demonstrate that if R is smaller than one, then there exists a unique disease- 0 free equilibrium that is both locally asymptotically stable by using the theorytools of fractional calculus, but whenR > 1 heendemicequilibrium is locallyasymptotically 0 stable. Furthermore, using a suitable of Lyapunov function, we will prove the global stability of the healthy equilibrium and establish sufficient requirements for both equilibrium point. Finally, we provide some numerical simulations to demonstrate our main findings.
Description
Keywords
fractional order derivative; epidemic model; stability analysis; the
time delay; numerical simulations