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. 
View via Publisher
dmi.unict.it
305 Citations
Highly Influential Citations
25
Background Citations
62
Methods Citations
48
Results Citations
4

Figures from this paper

305 Citations

On the Basic Reproduction Number of Reaction-Diffusion Epidemic Models

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

Basic Reproduction Numbers for a Class of Reaction-Diffusion Epidemic Models

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.

On a vector-host epidemic model with spatial structure

In this paper, we study a reaction–diffusion vector-host epidemic model. We define the basic reproduction number R0 and show that R0 is a threshold parameter: if the disease free equilibrium is…

A reaction–diffusion SIS epidemic model with saturated incidence rate and logistic source

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

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.

Analysis on a diffusive SIS epidemic model with saturated incidence rate and linear source in a heterogeneous environment

Dynamics of spatially heterogeneous viral model with time delay

A delayed reaction-diffusion virus model with a general incidence function and spatially dependent parameters is investigated. The basic reproduction number for the model is derived, and the uniform…

The principal eigenvalue for periodic nonlocal dispersal systems with time delay

Analysis of a diffusive epidemic system with spatial heterogeneity and lag effect of media impact

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

...

References

SHOWING 1-10 OF 40 REFERENCES

A reaction-diffusion SIS epidemic model in a time-periodic environment

In this paper, we consider a susceptible–infected–susceptible (SIS) reaction–diffusion model, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…

The effects of spatial heterogeneity in population dynamics

The dynamics of a population inhabiting a heterogeneous environment are modelled by a diffusive logistic equation with spatially varying growth rate. The overall suitability of an environment is…

Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model

To understand the impact of spatial heterogeneity of environment and movement of individuals on the persistence and extinction of a disease, a spatial SIS reaction-diffusion model is studied,…

On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations

It is shown that in certain special cases one can easily compute or estimate the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population.

A Nonlocal and Time-Delayed Reaction-Diffusion Model of Dengue Transmission

It turns out that the infection risk may be underestimated if the spatially averaged parameters are used to compute the basic reproduction number for spatially heterogeneous infections.

Threshold dynamics of an infective disease model with a fixed latent period and non-local infections

An infectious disease model containing a fixed latency and non-local infection caused by the mobility of the latent individuals in a continuous bounded domain is derived and it is shown that the model has the global threshold dynamics which predicts whether the disease will die out or persist.

Traveling Waves and Spread Rates for a West Nile Virus Model

A reaction–diffusion model for the spatial spread of West Nile virus is developed and analysed, and comparison theorem results are used to show that the spread rate of the simplified model may provide an upper bound for thespread rate of a more realistic and complex version of the model.

Uniqueness of the Bistable Traveling Wave for Mutualist Species

For a system of reaction–diffusion equations that models the interaction of n mutualist species, the existence of the bistable traveling wave solution has been proved where the nonlinear reaction…

Dynamics of an epidemic model with non-local infections for diseases with latency over a patchy environment

In this paper, with the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of the population may disperse, we formulate an SIR model with a…

Spatial Spread of Rabies Revisited: Influence of Age-Dependent Diffusion on Nonlinear Dynamics

This work shows how the distinction of territorial patterns between juvenile and adult foxes, the main carriers of the rabies under consideration, yields a class of partial differential equations involving delayed and nonlocal terms that are implicitly defined by a hyperbolic‐parabolic equation.