# Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models

@article{Wang2012BasicRN, title={Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models}, author={Wendi Wang and Xiao-Qiang Zhao}, journal={SIAM J. Appl. Dyn. Syst.}, year={2012}, volume={11}, pages={1652-1673} }

The theory of the principal eigenvalue is developed for an elliptic eigenvalue problem associated with a linear parabolic cooperative system with some zero diffusion coefficients. Then the basic reproduction number and its computation formulae are established for reaction-diffusion epidemic models with compartmental structure. These theoretical results are applied to a spatial model of rabies to study the influence of spatial heterogeneity and population mobility on disease transmission.

## 305 Citations

### On the Basic Reproduction Number of Reaction-Diffusion Epidemic Models

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The purpose of this paper is to investigate the basic reproduction number $R_0$ for spatial reaction-...

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Using matrix analysis, it is shown that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important cases that include, among others, a single infected compartment, constant diffusion rates, uniform diffusion patterns among the infected compartments, and partial diffusion in the system.

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A reaction–diffusion SIS epidemic model with saturated incidence rate and logistic source for the susceptible individuals is considered. We establish the uniform bounds of parabolic system and…

### Asymptotic Profiles of Basic Reproduction Number for Epidemic Spreading in Heterogeneous Environment

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- 2020

The effect of diffusion rates on the basic reproduction number of a general compartmental reaction-diffusion epidemic model in a heterogeneous environment is considered and it is shown the limit of thebasic reproduction number is the maximum value of the local reproduction number on the spatial domain.

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We considered an SIS functional partial differential model cooperated with spatial heterogeneity and lag effect of media impact. The wellposedness including existence and uniqueness of the solution…

### Threshold dynamics of an age-space structured SIR model on heterogeneous environment

- MathematicsAppl. Math. Lett.
- 2019

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