A mathematical model for a disease outbreak considering waning-immunity class with nonlinear incidence and recovery rates

Q1 Social Sciences

Journal of Biosafety and Biosecurity Pub Date : 2024-06-26 DOI:10.1016/j.jobb.2024.05.005

Nursanti Anggriani , Lazarus Kalvein Beay , Meksianis Z. Ndii , Fatuh Inayaturohmat , Sanubari Tansah Tresna

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引用次数: 0

Abstract

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 process. Additionally, the availability of medical resources limits the recovery rate of infected patients, adding further nonlinear dynamics to the healing process. Our research introduces novelty by combining nonlinear incidence and recovery rates alongside waning immunity in an epidemic model. We present a modified SIRW-type model, examining the epidemic problem with these factors. Through analysis, we explore conditions for non-endemic and co-existing cases based on the basic reproduction ratio. The local stability of equilibria is verified using the Routh-Hurwitz criteria, while global stability is assessed using Lyapunov functions for each equilibrium. Furthermore, we investigate bifurcations around both non-endemic and co-existing equilibria. Numerically, we give some simulations to support our analytical findings.

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考虑到非线性发病率和恢复率的免疫力减弱类疾病爆发数学模型

在传染病的传播过程中，干预水平对健康人和受感染者之间的互动起着至关重要的作用，从而导致非线性传播过程。此外，医疗资源的可用性也限制了感染者的康复率，进一步增加了治疗过程的非线性动态性。我们的研究将非线性发病率和康复率与免疫力减弱结合在一个流行病模型中，从而带来了新颖性。我们提出了一个改进的 SIRW 型模型，研究了包含这些因素的流行病问题。通过分析，我们探讨了基于基本繁殖率的非流行病例和共存病例的条件。我们使用 Routh-Hurwitz 准则验证了均衡的局部稳定性，同时使用每个均衡的 Lyapunov 函数评估了全局稳定性。此外，我们还研究了非地方性均衡和共存均衡周围的分岔。在数值上，我们给出了一些模拟来支持我们的分析结果。

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