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Global analysis of multi-host and multi-vector epidemic models
1Department of Mathematics, California State University, Fullerton, CA 92831, USA.
Abstract:
We formulate a multi-group and multi-vector epidemic model in which hosts' dynamics is captured by staged-progression framework and the dynamics of vectors is captured by an SI framework. The proposed model describes the evolution of a class of zoonotic infections where the pathogen is shared by m host species and transmitted by p arthropod vector species. In each host, the infectious period is structured into n stages with a corresponding infectiousness parameter to each vector species. We determine the basic reproduction number and investigate the dynamics of the systems when this threshold is less or greater than one. We show that the dynamics of the multi-host, multi-stage, and multi-vector system is completely determined by the basic reproduction number and the structure of the host-vector network configuration. Particularly, we prove that the disease-free equilibrium is globally asymptotically stable (GAS) whenever , and a unique strongly endemic equilibrium exists and is GAS if and the host-vector configuration is irreducible. That is, either the disease dies out or persists in all hosts and all vector species.
Insights
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.
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.
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