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Carrier-borne epidemic models incorporating population mobility
1Department of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne, United Kingdom.
Abstract:
A study was made of multigroup epidemic models in which individuals are able to move between groups, infectious contact occurring only between an infective and a susceptible in the same group. Because of the mathematical intractability of such models; we look mainly at the number of susceptibles directly contacted by the infectives that are initially introduced into the population, ignoring subsequent infections caused by these newly infected individuals. We thus have a generalization of the carrier-borne epidemic model of Weiss [Biometrics 21:481-491 (1965)]. We consider first a model in which only infectives are able to move, then one in which both infectives and susceptibles move between groups. In each case we study both deterministic and stochastic versions of the model, concentrating mainly on the effect of varying the speed at which individuals move between groups on the number of initial susceptibles contacted. For the case in which only infectives move, the model is compared with a suitably matched model in which there is no movement between groups but infectives are able to infect outside their own group. The paper concludes with remarks on the behavior of the epidemic process if initially susceptible individuals that become infected are able to contribute to the further spread of the disease.
Insights
This study simplifies complex multigroup epidemic models by focusing on initial infections. It reveals how movement speed between groups impacts disease spread among susceptible individuals.
Area of Science:
- Mathematical Epidemiology
- Population Dynamics
- Infectious Disease Modeling
Background:
- Multigroup epidemic models with intergroup mobility present significant mathematical challenges.
- Previous models, like Weiss's carrier-borne epidemic model, often lack detailed intergroup movement dynamics.
- Understanding how population movement influences disease transmission is crucial for public health.
Purpose of the Study:
- To analyze simplified multigroup epidemic models with intergroup mobility.
- To investigate the impact of movement speed on the initial spread of infectious diseases.
- To generalize and extend existing epidemic modeling frameworks.
Main Methods:
- Developed simplified deterministic and stochastic models focusing on initial infections.
- Examined two scenarios: infectives moving and both infectives and susceptibles moving between groups.
- Compared models with and without intergroup movement for infective-only mobility.
Main Results:
- The speed of movement between groups significantly affects the number of initial susceptible individuals contacted.
- Simplified models provide insights into epidemic dynamics despite mathematical intractability of full models.
- Movement patterns of infectious individuals play a key role in early-stage disease transmission.
Conclusions:
- Intergroup mobility is a critical factor in shaping epidemic trajectories.
- The study offers a generalized framework for analyzing epidemic spread in structured populations.
- Further research should consider the role of newly infected individuals in disease propagation.