Epidemics and underlying factors of multiple-peak pattern on hand, foot and mouth disease inWenzhou, China

Optimal Control Strategies of HFMD in Wenzhou, China

“…Similar to the models in [5,16,17,22], we can establish the following flowchart of compartments of HFMD (see Figure 2):…”

“…It should be noted that there are 11 undetermined parameters in R 0 , each with different mean value and variance (see Table 3 in Appendix), which means that it is tedious and extremely complex to study the effects of these parameters on the HFMD dynamics. In order to detect the underlying factors more simply, a better idea is to do the sensitivity analysis of different categories of parameters [22].…”

“…the Lipschitz property of the state system with respect to state variables S 1 , S 2 , E, I, L, and R (see [43,44]). For small final time T, the optimal control is given by (22) that is unique by the analysis above. Because the problems (10)-(13) are autonomous, uniqueness is valid for any time T and not only for small time T. □ e optimal control set predicted by eorems 2 and 3 represents the optimal intervention strategy, given the cost constraints, and can be found by the application of celebrated Pontryagin's maximum principle [42] and appropriate numerical methods [45].…”

“…. , 6, into formula (22). ey are not stored as the control variables u i , but as temporary vectors u i .…”

“…Zhou et al [21] investigated the epidemiological feature of HFMD in Wenzhou. Dai et al [22] had shown that the school opening and meteorological factors were primarily responsible for annual multiple-peak pattern of the outbreaks of HFMD in Wenzhou.…”