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Derdei Bichara1, Abderrahman Iggidr2

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This study introduces a flexible infectious disease model with multiple host groups and interaction patches. Increased patches and host mobility enhance disease spread, impacting prevalence and the basic reproduction number.

Keywords:
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Area of Science:

  • Mathematical modeling of infectious diseases
  • Epidemiological dynamics and host-pathogen interactions
  • Computational biology and simulation

Background:

  • Infectious disease transmission is complex, influenced by host population structure and spatial interactions.
  • Existing models often simplify host group structures and spatial dynamics.
  • Understanding the impact of host mobility on disease spread is crucial for effective control strategies.

Purpose of the Study:

  • To develop a comprehensive multi-patch, multi-group model for infectious disease dynamics.
  • To incorporate epidemiological status-dependent host mobility using a Lagrangian approach.
  • To analyze the effects of heterogeneity in groups, patches, and mobility on disease spread and key epidemiological parameters.

Main Methods:

  • Development of a novel multi-patch, multi-group mathematical model.
  • Application of a Lagrangian approach to model host mobility based on epidemiological status.
  • Derivation of the basic reproduction number (R0) for a general SEIRS (Susceptible-Exposed-Infectious-Recovered-Susceptible) model.
  • Exploration of heterogeneity effects through mathematical analysis and numerical simulations.

Main Results:

  • The basic reproduction number (R0) increases with the number of patches and host mobility.
  • Explicit determination of R0 when susceptible mobility matrices are rank one and stochastic, showing independence from mobility.
  • Identification of rank-one mobility matrices as capturing significant modeling scenarios.
  • Numerical simulations demonstrate the substantial impact of mobility patterns on disease prevalence and R0.

Conclusions:

  • Host group structure, spatial distribution (patches), and mobility patterns significantly influence infectious disease dynamics.
  • The developed model provides a flexible framework for studying complex epidemiological scenarios.
  • Mobility patterns are critical factors in determining disease prevalence and the potential for spread.