A realistic model for the periodic dynamics of the hand-foot-and-mouth disease

Abstract

<abstract><p>In this paper, an SEIQRS model with a periodic vaccination strategy is studied for the dynamics of the Hand-Foot-and-Mouth Disease (HFMD). This model incorporates a seasonal variation in the disease transmission rate $ \beta (t) $. Our model has a unique disease free periodic solution (DFPS). The basic reproductive number $ R_{0} $ and its lower and upper bounds, $ R_{0}^{inf} $ and $ R_{0}^{sup} $ respectively, are defined. We show that the DFPS is globally asymptotically stable when $ R_{0}^{sup} < 1 $ and unstable if $ R_{0}^{inf} > 1 $. Computer simulations of our model have been conducted using a novel periodic function of the contact rate. This novel function imitates the seasonality in the observed, multi-peaks pattern, data. Clear and good matching between real data and the obtained simulation results are shown. The obtained simulation results give a good prediction and possible control of the disease dynamics.</p></abstract>