Incorporating immunological ideas in epidemiological models.

Many diseases show important interactions between epidemiology and immunology. Both models and data suggest that epidemiologically controlled variables, like frequency and intensity of exposure, can affect immunological outcomes in a wide variety of diseases. Conversely, the results of the immunological "battle" between host and parasite determine the ability of the parasite to spread. I present a simple model with two possible states of infection, which assumes that higher exposure to infection is correlated with likelihood of acquiring a more severe infection. For some parameter values, this model leads to simultaneous stability of the disease-free equilibrium and an endemic equilibrium, implying that the disease might be able to persist in a population that it could not invade. I also derive a simple and interpretable sufficient condition for multiple stable states. The "cartoon" model presented here shows that interaction between epidemiology and immunology can have important effects on the invasion and persistence of diseases. In particular, it raises the possibility that this mechanism can lead to mathematical "catastrophe" and to long-term cycles in disease prevalence.