The data fitting and optimal control of a hand, foot and mouth disease (HFMD) model with stage structure

Currently, more than one million children suffer from hand, foot and mouth disease (HFMD) every year in China. And there are no effective vaccines or antiviral drugs specifically targeted HFMD. In this paper, a two stage-structured model is constructed to fit the HFMD data from 2009 to 2014 in China and obtain its optimal parameter values by the Chi-square test of statistical inference. Using the parameter values obtained can precisely and reliably forecast the clinical cases. The basic reproduction numbers for each year are more than unit, which suggests that HFMD will persist in China under the current conditions. Sensitivity analysis of the basic reproduction number is conducted to evaluate the effectiveness of HFMD control measures. Using Pontryagins maximum principle, we derive the necessary conditions for optimal control of HFMD. Further, the impact of combinations of the strategies on HFMD transmission is investigated. Finally, we find out the most cost-effective strategy though carrying out cost-effectiveness analysis.