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A PERIODIC ROSS-MACDONALD MODEL IN A PATCHY ENVIRONMENT.

Daozhou Gao1, Yijun Lou2, Shigui Ruan3

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Summary
This summary is machine-generated.

This study introduces a periodic malaria model accounting for time and space variations in disease spread. Controlling travel between regions can significantly impact malaria prevalence.

Keywords:
Malariabasic reproduction numberpatch modelseasonalitythreshold dynamics

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Disease Modeling

Background:

  • The classical Ross-Macdonald model provides a foundation for understanding malaria transmission dynamics.
  • Temporal and spatial heterogeneity are crucial factors influencing infectious disease spread but are often simplified in models.

Purpose of the Study:

  • To develop a periodic malaria model that incorporates both temporal and spatial heterogeneity in disease transmission.
  • To analyze the impact of these heterogeneities on malaria dynamics and identify potential control strategies.

Main Methods:

  • Utilizing a multi-patch structure to represent spatial heterogeneity, with individuals traveling between patches.
  • Incorporating time-periodic coefficients to describe temporal heterogeneity in disease transmission.
  • Calculating the basic reproduction number ([Formula: see text]) to determine disease persistence.

Main Results:

  • The model demonstrates that the disease-free periodic solution is globally asymptotically stable when [Formula: see text].
  • Conversely, a positive periodic solution (indicating sustained malaria transmission) is globally asymptotically stable when [Formula: see text].
  • Numerical simulations confirm analytical findings and highlight the influence of travel patterns on disease prevalence.

Conclusions:

  • The proposed periodic malaria model effectively captures the complexities of temporal and spatial heterogeneity.
  • The basic reproduction number serves as a critical threshold for malaria eradication or persistence.
  • Travel control strategies, informed by this model, can be a viable approach to managing malaria prevalence.