Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (1): 201-215.

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A Dengue Fever Model Incorporating Heterogeneous Cross-Diffusion

Min Zhu*(),Mengli Liu()   

  1. School of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241000
  • Received:2021-03-23 Online:2022-02-26 Published:2022-02-23
  • Contact: Min Zhu E-mail:min_zhuly@163.com;liumengli_zz@163.com
  • Supported by:
    the NSFC(11801009);the Initial Scientific Research Fund of Doctor in Anhui Normal University(751993)

Abstract:

To describe the mutual diffusion phenomenon between human and mosquitoes in the spread and control of dengue fever, we introduce more complex heterogeneous cross-diffusion into the dengue fever model, and explore the impact of cross-diffusion on its dynamics. In view of the contagion risk threshold, we are devoted to analyzing the existence and non-existence of coexistence solution for the steady state. The findings show that if the contagion risk threshold is greater than one associated with some conditions, this scenario is disadvantage to the control of dengue fever, as it will lead to the coexistence of the viruses carried by human and by mosquitoes. Some epidemiological explanations are presented finally.

Key words: Dengue model, Heterogeneous cross-diffusion, Coexistence solution, Contagion risk threshold

CLC Number: 

  • O175.21
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