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Diseases with a Chronic Stage in a Population with Varying Size

Maia Martcheva
Polytechnic University, (Brooklyn NY)

In this paper we consider an epidemiological model of Hepatitis C infection which is characterized by chronic stage. The model is homogeneous of degree one. We consider both a version where the chronic stage is structured by the age of infection and the ordinary differential equations counterpart. We completely analyze the ODE model and show that the endemic proportions are stable and no oscillations are possible. In the structured case we find out that zero can be a solution of the characteristic equation and our simulations suggest that in this case the endemic equilibrium is not stable. Both models have similar behavior around the disease-free equilibrium, namely the disease-free equilibrium is globally asymptotically stable. We propose a numerical method for the infection-age-structured model and show that it is consistent and convergent of first order. We include some results of the simulations based on the numerical method.

Joint work with Carlos Castillo-Chavez.

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1998-1999 Mathematics in Biology

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