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Disease emergence in multi-host epidemic models
Robert K McCormack1, Linda J S Allen
1Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA. rmccormack16@hotmail.com
Abstract:
Most pathogens are capable of infecting multiple hosts. These multiple hosts provide many avenues for the disease to emerge. In this investigation, we formulate and analyse multi-host epidemic models and determine conditions under which the disease can emerge. In particular, SIS and SIR epidemic models are formulated for a pathogen that can infect n different hosts. The basic reproduction number is computed and shown to increase with n, the number of hosts that can be infected. Therefore, the possibility of disease emergence increases with the number of hosts infected. The SIS model for two hosts is studied in detail. Necessary and sufficient conditions are derived for the global stability of an endemic equilibrium. Numerical examples illustrate the dynamics of the two- and three-host epidemic models. The models have applications to hantavirus in rodents and other zoonotic diseases with multiple hosts.
Insights
The emergence of infectious diseases increases with the number of hosts a pathogen can infect. This study develops multi-host epidemic models to understand disease spread and emergence conditions.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Dynamics
Background:
- Pathogens often infect multiple hosts, creating diverse transmission routes.
- Understanding multi-host pathogen dynamics is crucial for predicting and controlling disease emergence.
Purpose of the Study:
- To formulate and analyze multi-host epidemic models (SIS and SIR).
- To determine conditions for disease emergence in multi-host systems.
- To investigate the impact of the number of hosts on disease spread.
Main Methods:
- Formulation of Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) epidemic models for 'n' hosts.
- Computation of the basic reproduction number (R0).
- Analysis of the global stability of endemic equilibria for the two-host SIS model.
Main Results:
- The basic reproduction number increases with the number of hosts ('n').
- The likelihood of disease emergence is positively correlated with the number of infected hosts.
- Conditions for the global stability of endemic states were derived for the two-host model.
Conclusions:
- Increasing the number of hosts amplifies the potential for infectious disease emergence.
- The developed models provide insights into zoonotic diseases like hantavirus.
- Mathematical modeling is essential for understanding complex epidemiological patterns in multi-host systems.
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