Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic
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ORIGINAL PAPER
Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic Omar Khyar · Karam Allali
Received: 11 April 2020 / Accepted: 29 August 2020 © Springer Nature B.V. 2020
Abstract This paper investigates the global stability analysis of two-strain epidemic model with two general incidence rates. The problem is modelled by a system of six nonlinear ordinary differential equations describing the evolution of susceptible, exposed, infected and removed individuals. The wellposedness of the suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points are given, namely the disease-free equilibrium, the endemic equilibrium with respect to strain 1, the endemic equilibrium with respect to strain 2, and the last endemic equilibrium with respect to both strains. By constructing suitable Lyapunov functional, the global stability of the disease-free equilibrium is proved depending on the basic reproduction number R0 . Furthermore, using other appropriate Lyapunov functionals, the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number R01 and the strain 2 reproduction number R02 . Numerical simulations are performed in order to confirm the different theoretical results. It was observed that the model with a generalized incidence functions encompasses a large number of models with classical incidence functions and it gives a significant wide view about the equilibria stability. Numerical comparison between the model results and COVID-19 O. Khyar (B) · K. Allali Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, PO Box 146, Mohammedia, Morocco e-mail: [email protected]
clinical data was conducted. Good fit of the model to the real clinical data was remarked. The impact of the quarantine strategy on controlling the infection spread is discussed. The generalization of the problem to a more complex compartmental model is illustrated at the end of this paper. Keywords Global stability analysis · SEIR · General incidence function · Multi-strain epidemic model · Basic reproduction number · COVID-19
1 Introduction Nowadays, several infectious diseases are still targeting huge populations. They are considered amongst the principal causes of mortality, especially in many developing countries. Accordingly, mathematical modelling in epidemiology occupies more and more an increasingly preponderant place in public health research. This research discipline contributes indeed to well understand the studied epidemiological phenomenon and apprehend the different factors that can lead to a severe epidemic or even to a dangerous pandemic worldwide. The classical susceptible-infected-recovered (SIR) epidemic model was first introduced in [1]. Nevertheless, in many cases, the infection incubation period may take a long time interval. In this period, an incubated individual remains latent but not y
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