Switching Control Strategies

Liu, Xinzhi; Stechlinski, Peter

This chapter is motivated by the application of control strategies to eradicate epidemics. In part, the previous switched epidemic models are reintroduced with continuous (e.g., vaccination of newborns continuously in time) or switching control (i.e., piecewise continuous application of vaccination or treatment schemes) for evaluation and optimization. As discussed earlier, infectious disease models are a crucial component in designing and implementing detection, prevention, and control programs (e.g., the World Health Organization’s program against smallpox, leading to its global eradication by 1977). The switched SIR model is first returned to for consideration and analysis of vaccination of the susceptible group (e.g., newborns or the entire cohort). Subsequently, the developed theoretical methods are applied to the switched SIR model with a treatment program in effect. Common Lyapunov functions are used to provide controlled eradication of diseases modeled by the so-called SEIR (Susceptible-Exposed-Infected-Recovered) model with seasonal variations captured by switching. A screening process, where traveling individuals are examined for infection, is proposed and studied for the switched multi-city model of the previous chapter. Switching control of diseases such as Dengue and Chikungunya which are spread via mosquito–human interactions, is investigated.