A simple two-strain HSV epidemic model with palliative treatment

J. Kwakye, J. Tchuenche
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引用次数: 0

Abstract

A two-strain model of the transmission dynamics of herpes simplex virus (HSV) with treatment is formulated as a deterministic system of nonlinear ordinary differential equations. The model is then analyzed qualitatively, with numerical simulations provided to support the theoretical results. The basic reproduction number \(R_0\) is computed with \(R_0=\text{max}\lbrace R_1, R_2 \rbrace \) where \(R_1\) and \(R_2\) represent respectively the reproduction number for HSV1 and HSV2. We also compute the invasion reproductive numbers \(\tilde{R}_1\) for strain 1 when strain 2 is at endemic equilibrium and \(\tilde{R}_2\) for strain 2 when strain 1 is at endemic equilibrium. To determine the relative importance of model parameters to disease transmission, sensitivity analysis is carried out. The reproduction number is most sensitive respectively to the contact rates \(\beta_1\), \(\beta_2\) and the recruitment rate \(\pi\). Numerical simulations indicate the co-existence of the two strains, with HSV1, dominating but not driving out HSV2 whenever \(R_1 > R_2 > 1\) and vice versa.
一个简单的具有姑息治疗的两株HSV流行模型
将单纯疱疹病毒(HSV)在治疗过程中的传播动力学的两株模型公式化为非线性常微分方程的确定系统。然后对模型进行了定性分析,并提供了数值模拟来支持理论结果。基本再现数\(R_0\)是用\(R_0=\text{max}\lbrace R_1,R_2\rbrace\)计算的,其中\(R_1\)和\(R_2\)分别表示HSV1和HSV2的再现数。我们还计算了入侵繁殖数量{R}_1\)对于菌株1,当菌株2处于地方性平衡时{R}_2\)对于菌株2,当菌株1处于地方性平衡时。为了确定模型参数对疾病传播的相对重要性,进行了敏感性分析。繁殖数分别对接触率(β_1)、(β_2)和募集率(π)最敏感。数值模拟表明,无论何时(R_1>R_2>1),这两种菌株都共存,其中HSV1占主导地位,但不会驱逐HSV2,反之亦然。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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10
审稿时长
8 weeks
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