Analysis of a virus mutation epidemic model with vertical transmission

GAO Wenzhe; LUO Zhixue; CHENG Xin

doi:10.13471/j.cnki.acta.snus.ZR20250166

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Analysis of a virus mutation epidemic model with vertical transmission

Research articles | 更新时间：2025-11-25

- Analysis of a virus mutation epidemic model with vertical transmission
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 6, Pages: 160-168(2025)
- 作者机构：
  
  1.安康学院数学与统计学院，陕西安康 725000
  2.兰州交通大学数理学院，甘肃兰州 730070
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20250166
  CLC： O175.1
- Received：06 August 2025，
  
  Revised：2025-09-27，
  
  Accepted：30 September 2025，
  
  Published Online：23 October 2025，
  
  Published：25 November 2025
- 稿件说明：
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高文哲,雒志学,程鑫.具有垂直传染的病毒变异传染病模型分析[J].中山大学学报(自然科学版)(中英文),2025,64(06):160-168.

GAO Wenzhe,LUO Zhixue,CHENG Xin.Analysis of a virus mutation epidemic model with vertical transmission[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(06):160-168.
高文哲,雒志学,程鑫.具有垂直传染的病毒变异传染病模型分析[J].中山大学学报(自然科学版)(中英文),2025,64(06):160-168. DOI： 10.13471/j.cnki.acta.snus.ZR20250166.

GAO Wenzhe,LUO Zhixue,CHENG Xin.Analysis of a virus mutation epidemic model with vertical transmission[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(06):160-168. DOI： 10.13471/j.cnki.acta.snus.ZR20250166.

摘要

本文以COVID-19为背景，在年龄结构的传染病问题中，首次考虑三类人群同时具有传染性的情况，建立一类具有垂直传染和潜伏期的病毒变异传染病模型.　首先利用微分方程定性理论证得模型非负解的存在唯一性，并给出疾病流行的基本再生数.　接着，借助微分方程稳定性理论，证明得到无病平衡点存在与稳定的充分条件.　最后证明得到地方病平衡点的存在性.

Abstract

Against the backdrop of COVID-19， we consider the scenario where three groups of people are simultaneously infectious in the age-structured infectious disease problem， it was established that a virus mutation epidemic model with vertical transmission and latency period. Firstly， the existence and uniqueness of non-negative solutions are proved， and the basic regeneration number of the model was obtained by using the qualitative theory of ordinary differential equation. Secondly， the sufficient conditions for the existence and stability of the disease-free equilibrium point are proved by using the stability theory of ordinary differential equationv. Finally， the existence of the endemic equilibrium point is demonstrated.

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references

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