Modeling diseases with latency and relapse - P. van den Driessche; Lin Wang; Xingfu Zou (Mathematical Biosciences and Engineering)
A general mathematical model for a disease with an exposed(latent) period and relapse is proposed. Such a model isappropriate for tuberculosis, including bovine tuberculosis incattle and wildlife, and for herpes. For this model with ageneral probability of remaining in the exposed class, the basicreproduction number $\R_0$ is identified and its thresholdproperty is discussed. In particular, the disease-free equilibriumis proved to be globally asymptotically stable if $\R_01$, and the disease is shown to be uniformly persistentwith the infective population size either approaching oroscillating about the endemic level. Numerical simulations (forparameters appropriate for bovine tuberculosis in cattle) with$\mathcal{R}_0>1$ indicate that solutions tend to this endemicstate.