Discrete-time and continuous-time models with applications to the spread of hantavirus in wild rodent and human populations
Wesley, Curtis L.
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Hantavirus is a viral zoonotic disease carried by wild rodents (rats and mice) and spread to human via viral contaminated soil. Three distinct hantavirus epidemic modeling projects are studied in this investigation. The first project involves deterministic and stochastic discrete-time models structured by the stages of the infection, age and sex of the rodent. The basic reproduction number R0, the threshold for disease extinction, is computed for the deterministic model and a condition for permanence of a simplified male-only model is discussed. Numerical examples contrast the results of the deterministic and stochastic models. The second project focuses on some deterministic and stochastic models for hantavirus infection in rodents with transmission to humans via viral-contaminated soil. We study a rodent model with constant birth rate and carrying capacity. We calculate R0 and analyze existence and stability of disease-free and endemic equilibria. Also, we consider a rodent model with periodic birth and carrying capacity. We calculate an average basic reproduction number &R0tilde; based on average birth rate and average population size for the periodic model. Numerical examples illustrate the dynamics of the deterministic and stochastic models. Lastly, the goal of the third project is to analyze some nonautonomous seasonal epidemic models. For the seasonal models, it is shown that the time-averaged basic reproduction number is a threshold for disease extinction when the population demographics are periodic.