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Global analysis of multi-host and multi-vector epidemic models.

Derdei Mahamat Bichara1

  • 1Department of Mathematics, California State University, Fullerton, CA 92831, USA.

Journal of Mathematical Analysis and Applications
|April 15, 2020
PubMed
Summary

This study introduces a complex epidemic model for zoonotic diseases involving multiple host and vector species. The model shows that disease spread depends on the basic reproduction number and host-vector interactions, determining if the disease dies out or persists.

Keywords:
Global stabilityGraph theoryLyapunov functionsMigrationVector-borne diseases

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Disease Ecology

Background:

  • Zoonotic infections involve pathogens shared between animal hosts and arthropod vectors.
  • Understanding transmission dynamics is crucial for disease control and public health.
  • Existing models often simplify host or vector components, limiting applicability to complex ecological systems.

Purpose of the Study:

  • To develop and analyze a comprehensive mathematical model for multi-host, multi-vector zoonotic diseases.
  • To investigate the role of staged progression in hosts and SI dynamics in vectors.
  • To determine the conditions for disease persistence or eradication based on epidemiological parameters.

Main Methods:

  • Formulation of a multi-group, multi-vector epidemic model.
  • Incorporation of staged-progression framework for host dynamics.
  • Application of an SI (Susceptible-Infectious) framework for vector dynamics.
  • Calculation and analysis of the basic reproduction number (R0).

Main Results:

  • The model's dynamics are fully characterized by the basic reproduction number and host-vector network structure.
  • Disease-free equilibrium is globally asymptotically stable when R0 is less than one.
  • A unique, strongly endemic equilibrium exists and is globally asymptotically stable when R0 is greater than one and the host-vector configuration is irreducible.

Conclusions:

  • The study provides a robust framework for analyzing complex zoonotic disease systems.
  • Disease outcomes (eradication or persistence) are predictable based on R0 and network properties.
  • This model aids in understanding and managing zoonotic diseases in diverse ecological settings.