Global stability for a delayed multi-group SIRS epidemic model with cure rate and incomplete recovery rate

In this paper, strongly connected and non-strongly connected multi-group viral models with time delays and general incidence functions are considered. Employing the Lyapunov functional method and a graph-theoretic approach, we show that the global dynamics of the strongly connected system are determined by the basic reproduction number under some reasonable conditions for incidence functions. In addition, we find a more complex and more interesting result for multi-group viral models with non-strongly connected networks because of the basic reproduction numbers corresponding to each strongly connected component. Finally, we provide simulations for non-strongly connected multi-group viral models to support our conclusion.

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Global stability of multi-group viral models with general incidence functions

Fan

Hao

Sun

2017

J. Math. Biol.

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Fractional-order SIR epidemic model with treatment cure rate

Sadki,

Harroudi,

Allali

2023

Partial Differential Equations in Applied Mathematics

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Simplicial SIRS epidemic models with nonlinear incidence rates

Wang

Zhao

Luo

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Mathematical epidemiology that describes the complex dynamics on social networks has become increasingly popular. However, a few methods have tackled the problem of coupling network topology with complex incidence mechanisms. Here, we propose a simplicial susceptible-infected-recovered-susceptible (SIRS) model to investigate the epidemic spreading via combining the network higher-order structure with a nonlinear incidence rate. A network-based social system is reshaped to a simplicial complex, in which the spreading or infection occurs with nonlinear reinforcement characterized by the simplex dimensions. Compared with the previous simplicial susceptible-infected-susceptible (SIS) models, the proposed SIRS model can not only capture the discontinuous transition and the bistability of a complex system but also capture the periodic phenomenon of epidemic outbreaks. More significantly, the two thresholds associated with the bistable region and the critical value of the reinforcement factor are derived. We further analyze the stability of equilibrium points of the proposed model and obtain the condition of existence of the bistable states and limit cycles. This work expands the simplicial SIS models to SIRS models and sheds light on a novel perspective of combining the higher-order structure of complex systems with nonlinear incidence rates.

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Global stability for a delayed multi-group SIRS epidemic model with cure rate and incomplete recovery rate

Cited by 6 publications

References 28 publications

Global stability of multi-group viral models with general incidence functions

Global stability of multi-group viral models with general incidence functions

Fractional-order SIR epidemic model with treatment cure rate

Simplicial SIRS epidemic models with nonlinear incidence rates

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