Stability analysis and optimal control of a hand-foot-mouth disease (HFMD) model

Modelling the effects of contaminated environments on HFMD infections in mainland China

“…All other parameters are as shown in Table 1. transmission via free-living stages have substantial influence on the basic reproduction number of model (1). Note that our estimate of the basic reproduction number is greater than that obtained by the previous literature (Yang et al, 2013), who estimated the basic reproduction number as 1.392. This is because our proposed model includes both the indirect transmission via free-living viruses in the environment and asymptomatic infected individuals, which further consolidates the conclusion on the significant contribution of asymptomatic infected individuals and contaminated environments on transmission of HFMD.…”

“…(Ma et al, 2013) formulated a more realistic model in which the infectious individuals are classified into two compartments: infected and asymptomatic recessive, to investigate the seasonal spread of HFMD in Shandong Province. (Yang et al, 2013) analyzed the transmission dynamics with the aim of determining better control strategies through sensitivity analysis. However, the existing mathematical models only considered direct transmission between susceptible and infected individuals.…”

Analysis of a Hand-Foot-Mouth Disease Model with Standard Incidence Rate and Estimation for Basic Reproduction Number

“…The group of viruses includes polioviruses, coxsackieviruses, echoviruses and enteroviruses. Among these types of viruses, coxsackievirus A16 (COX A16) and enteroviruses 71 (EV71) are the most common ones to induce HFMD [1]. Since the first HFMD case was reported in New Zealand in 1957, this disease is now endemic worldwide.…”

“…Mathematical models are now applied to analyze the transmission and control of HFMD aimed to enable a better decision making for health policy makers [1,[3][4][5][6][7][8][9][10]. For example, the following HFMD model was constructed in [1] …”

“…In Models (1) and (2), the variable S, E, I, R, Q means the number of the susceptible, the exposed, the infective, the recovered, the quarantined individuals, respectively. The basic reproduction number, the local and global stability of the equilibrium, and the optimal control of Model (1) were analyzed in [1]. We note that only numerical simulations were given in [7] to analyze the transmission of HFMD.…”