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- Herbert W. Hethcote
- SIAM Review
- 2000

Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number R 0 , the contact number σ, and the replacement number R are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for R 0 are… (More)

- Herbert W Hethcote, Wendi Wang, Litao Han, Zhien Ma
- Theoretical population biology
- 2004

A predator-prey model with logistic growth in the prey is modified to include an SIS parasitic infection in the prey with infected prey being more vulnerable to predation. Thresholds are identified which determine when the predator population survives and when the disease remains endemic. For some parameter values the greater vulnerability of the infected… (More)

- H W Hethcote, P van den Driessche
- Journal of mathematical biology
- 1995

The SIS epidemiological model has births, natural deaths, disease-related deaths and a delay corresponding to the infectious period. The thresholds for persistence, equilibria and stability are determined. The persistence of the disease combined with the disease-related deaths can cause the population size to decrease to zero, to remain finite, or to grow… (More)

- Sara Y. Del Valle, James M. Hyman, Herbert W. Hethcote, Stephen Eubank
- Social Networks
- 2007

We present a method for estimating transmission matrices that describe the mixing and the probability of infection between age groups. Transmission matrices can be used to estimate age-dependent forces of infection in age-structured, compartmental models for the study of infectious diseases. We have analyzed the social network generated by bipartite graphs… (More)

- X Lin, H W Hethcote, P van den Driessche
- Mathematical biosciences
- 1993

A model for HIV transmission is formulated for a homosexual population of varying size, with recruitment into the susceptible class proportional to the active population size and with stages of progression to AIDS. Analysis of this model includes identifying the threshold that determines whether the disease dies out or proportions remain endemic and… (More)

- Simon A. Levin, Fred Brauer, +20 authors Angel F. Capurro
- 2007

Intraspecific competition, dispersal and disease dynamics in discrete-time patchy environments The impact of long-range dispersal on the rate of spread in population and epidemic models

- Gerardo Chowell, Ariel Cintrón-Arias, +5 authors Carlos Castillo-Chávez
- 2005

Efforts to anticipate, prevent, or control deliberate releases of biological agents are critical components of homeland security research. The lack of data on deliberately induced epidemics naturally leads to the use of mathematical models (capable of simulating realistic scenarios) in the evaluation of policies that ensure our security. Modeling single… (More)

- Tong Li, Yi Li, Herbert W. Hethcote
- Mathematical and Computer Modelling
- 2009

Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infection wave fronts arise by Hopf bifurcation for some spatial models for infectious disease transmission with distributed-contacts. Periodic traveling waves are shown to exist for the spatial analog of… (More)

- Wendi Wang, Yi Li, Herbert W. Hethcote
- I. J. Bifurcation and Chaos
- 2006

A host-parasite model is proposed that incorporates a nonlinear incidence rate. Under the influence of multiple infectious attacks, the model admits bistable regions such that the infection dies out if initial states lie in one region, and the population and parasites coexist if initial states lie in the other region. It is also found that parasites can… (More)

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