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A mathematical model for a disease outbreak considering waningimmunity class with nonlinear incidence and recovery rates

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Journal of Biosafety and Biosecurity 2024年第3期6卷 170-180页

作者： Nursanti Anggriani Lazarus Kalvein Beay Meksianis Z.Ndii Fatuh Inayaturohmat Sanubari Tansah Tresna Department of Mathematics Universitas PadjadjaranSumedangIndonesia Department of Mathematics Universitas PattimuraMalukuIndonesia Department of Mathematics Universitas Nusa CendanaKupangIndonesia

In the spread of infectious diseases,intervention levels play a crucial role in shaping interactions between healthy and infected individuals,leading to a nonlinear transmission ***,the availability of medical resources limits the recovery rate of infected patients,adding further nonlinear dynamics to the healing *** research introduces novelty by combining nonlinear incidence and recovery rates alongside waning immunity in an epidemic *** present a modified SIRW-type model,examining the epidemic problem with these *** analysis,we explore conditions for non-endemic and co-existing cases based on the basic reproduction *** local stability of equilibria is verified using the Routh-Hurwitz criteria,while global stability is assessed using Lyapunov functions for each ***,we investigate bifurcations around both non-endemic and co-existing ***,we give some simulations to support our analytical findings.

关键词： SIRW-type model Basic reproduction ratio Waning immunity nonlinear incidence rate nonlinear recovery rate Lyapunov functions Bifurcation

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Complex dynamics of a discrete-time SIR model with nonlinear incidence and recovery rates

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生物数学学报:英文版 2023年第8期16卷 1-45页

作者： Xiao Yu Ming Liu Zhaowen Zheng Dongpo Hu School of Mathematical Sciences Qufu Normal University Qufu 273165 P.R.China

In this paper,a discrete-time SIR epidemic model with nonlinear incidence and recovery rates is obtained by using the forward Euler’s *** existence and stability of fixed points in this model are well *** center manifold theorem and bifurcation theory are applied to analyze the bifurcation properties by using the discrete time step and the intervention level as control *** discuss in detail some codimension-one bifurcations such as transcritical,period-doubling and Neimark–Sacker bifurcations,and a codimension-two bifurcation with 1:2 *** addition,the phase portraits,bifurcation diagrams and maximum Lyapunov exponent diagrams are drawn to verify the correctness of our theoretical *** is found that the numerical results are consistent with the theoretical *** interestingly,we also found other bifurcations in the model during the numerical simulation,such as codimension-two bifurcations with 1:1 resonance,1:3 resonance and 1:4 resonance,generalized period-doubling and fold-flip *** results show that the dynamics of the discrete-time model are richer than that of the continuous-time SIR epidemic *** a discrete-time model may not only be widely used to detect the pathogenesis of infectious diseases,but also make a great contribution to the prevention and control of infectious diseases.

关键词： Discrete-time SIR epidemic model nonlinear incidence rate nonlinear recovery rate codimension-one bifurcation codimension-two bifurcation

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