Abstract
Immuno-epidemiological modeling of infectious diseases is a technique that links a within-host mathematical model with a between-host mathematical model. In the simplest nested models the within-host model is an ODE structured by the time since infection. The between-host model is a time-since-infection and chronological time structured PDE. The nested immuno-epidemiological are related to age-since-infection models that we consider in Chap. 8. The linking between the two models consists in two parts: linking through the time-since-infection and linking through the parameters of the epidemiological model which depend on the within-host variables. It is very important that the within-host model and the between-host model are consistent. For instance, if the disease is chronic, the within-host model should lead to chronic infection, that is have a stable infected equilibrium, and the between-host model should contain no recovered class. Such is the case with HIV. On the other hand, if the disease always leads to recovery, the within-host model should be an outbreak model, while the between-host model should have a recovered class. This scenario is appropriate for diseases such as influenza.
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Li, XZ., Yang, J., Martcheva, M. (2020). Nested Immuno-Epidemiological Models. In: Age Structured Epidemic Modeling. Interdisciplinary Applied Mathematics, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-030-42496-1_3
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