Epidemic Models with Switching

In this chapter, the methods developed thus far are applied to a variety of infectious disease models with different physiological and epidemiological assumptions. Many of the previous results are immediately applicable, thanks to the flexibility of the simple techniques used here. However, some complicating modeling assumptions lead to a need for different switched systems techniques not present in the previous chapter. First, the so-called SIS model is considered, followed by incorporation of media coverage, network epidemic models with interconnected cities (or patches), and diseases spread by vector agents (e.g., mosquitoes) which are modeled using time delays. Straightforward extensions of eradication results are given for models with vertical transmission, disease-induced mortality, waning immunity, passive immunity, and a model with general compartments.