Latent Infection Of Dynamic Model Of Hand, Foot And Mouth Disease

Hand, foot and mouth disease （HFMD） is common infectious disease among infant andchildren. HFMD is caused by a group of enterovirus which mainly include coxsackievirusA16（CA16） and enterovirus71（EV71）. It is estimated that500,000～1,800,000cases havebeen infected with HFMD per year in China after2008, it becomes more and more seriousand a major public-heath problem.HFMD afects mainly in children under10years old, but may also occur in adults.It can be transmitted to other person through direct contact with the infected individualor touch objects and surfaces which are touched by infected individual. The weekly dateof HFMD cases reported by the Department of Health of Shandong Province exhibits inthe summer and spring （April-october）are signifcantly higher than in winter and autumn.Within the perspective of the regional distribution of HFMD infected cases, there is not aobvious features. So far, most research on HFMD has been focused on the felds such asmolecular biology, clinical medicine, pathogeny and epidemiology, however, few literaturemakes use of the dynamical model to study the HFMD in China. This paper makes thefollowing researches:1. Considering that the Hand, foot and mouth often afects infant and children, at least98%of the patients are less than10, most adults will not exhibit the symptom （the recessive）.As a result, we built an S₁E₁I₁I₁^eQR₁S₂E₂I₂R₂non-autonomous dynamical model includingthe recessive infection and age-structure. After evaluating the basic reproduction number,we demonstrate the disease-free equilibrium is global asymptotically stable by appropriateLiapunov function, and analyze the disease is uniform Persistence when R0>1, then westudy the existence of the non-negative equilibrium.2. Considering the seasonality of HFMD cases, based on the HFMD data from theDepartment of Health of Shandong Province, this paper propose a dynamic model withperiodic transmission rates to investigate the seasonal HFMD. After evaluating the basicreproduction number, we analyze the dynamical behavior of the model and simulate the data of Shandong Province. By carrying out sensitivity analysis of the basic reproductionnumber on some parameters, we fnd that the recessive infection plays an important role inthe spread of HFMD, and only quarantine has little efect to control the disease.