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Population size dependent incidence in models for diseases without immunity
1Department of Mathematics, University of Iowa, Iowa City 52242.
Journal of Mathematical Biology
|January 1, 1994
Summary
This study analyzes SIS epidemiological models with population-dependent contact rates. Disease persistence significantly impacts population dynamics, potentially leading to extinction or reduced growth.
Area of Science:
- Mathematical epidemiology
- Population dynamics modeling
Background:
- Susceptible-Infectious-Susceptible (SIS) models are fundamental in epidemiology.
- Understanding disease dynamics requires incorporating population size and demographic factors.
Purpose of the Study:
- To analyze SIS epidemiological models with a contact rate dependent on total population size.
- To investigate the impact of disease persistence on population dynamics under various demographic structures.
Main Methods:
- Analysis of SIS epidemiological models.
- Determination of thresholds, equilibria, and stability.
- Incorporation of demographic structures: recruitment-death, generalized logistic, decay, and growth.
Main Results:
- Disease persistence, disease-related deaths, and reduced reproduction significantly affect population dynamics.
- Potential outcomes include population extinction (size to zero) or stabilization at a reduced size below carrying capacity.
- The exponential growth rate constant of the population can be decreased.
Conclusions:
- Epidemiological disease dynamics, when integrated with population-level factors, can lead to substantial alterations in population size and growth.
- The interplay between disease and population demographics is crucial for predicting long-term ecological outcomes.