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Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
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An almost periodic Ross-Macdonald model with structured vector population in a patchy environment.

Bin-Guo Wang1, Lizhong Qiang2, Zhi-Cheng Wang2

  • 1School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People's Republic of China. wangbinguo@lzu.edu.cn.

Journal of Mathematical Biology
|October 28, 2019
PubMed
Summary

This study introduces an almost periodic Ross-Macdonald model to analyze disease transmission in patchy environments. The findings indicate disease persistence or extinction based on the basic reproduction ratio, with implications for control strategies.

Keywords:
Almost periodicityBasic reproduction ratioMalaria transmissionPatch modelSkew-product semiflow

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Area of Science:

  • Mathematical epidemiology
  • Vector-borne disease dynamics
  • Ecological modeling

Background:

  • Understanding disease dynamics in heterogeneous environments is crucial for effective control.
  • Age structure in vector populations significantly influences disease transmission.
  • Patchy environments and host migration add complexity to epidemiological models.

Purpose of the Study:

  • To develop and analyze an almost periodic Ross-Macdonald model incorporating vector age structure in a patchy environment.
  • To establish a threshold criterion for disease persistence and extinction based on the basic reproduction ratio.
  • To investigate the impact of environmental factors and control strategies on disease transmission.

Main Methods:

  • Derivation of the basic reproduction ratio (R0) for the proposed model.
  • Analysis of the global dynamics using threshold-type results.
  • Numerical simulations to explore the effects of biting rate, human migration, and vector maturation period.

Main Results:

  • Disease persistence is guaranteed if R0 > 1, while extinction occurs if R0 < 1.
  • Biting rate significantly impacts disease transmission; human migration can reduce transmission risk.
  • Prolonging the vector maturation period is beneficial for disease control, with a computable threshold for outbreak.

Conclusions:

  • The derived threshold dynamics provide a basis for disease management strategies.
  • Numerical insights highlight the importance of vector maturation period and migration control.
  • Almost periodic models offer a more nuanced understanding of disease transmission compared to simple periodic models.