Dynamic Model Of Hand,Foot And Mouth Disease Considering Climate,Environmental Influences And Behavioral Habits

Hand,foot,and mouth disease（HFMD）affects more than one million people in China annually,with multi-wave outbreaks in some areas.The mechanism still needs to be clarified.We investigate the influence of climate,environmental factors（（i）temperature,（ii）relative humidity）,and human behavioral factors（iii）school opening and close on multi-wave outbreaks of HFMD.According to the transmission characteristics of HFMD and the epidemic situation in Shanghai,we establish a dynamic model of HFMD.Then,a distributed lag nonlinear model（DLNM）is set to obtain the relationship between temperature,relative humidity,and the transmission rateβ（t）.Then,the transmission rate is substituted into the dynamic model.Subsequently,the dynamic model is fitted with the reported case data of HFMD to verify the model’s effectiveness and compare and analyze the importance of the three periodicity factors.Finally,the optimal control problem of the HFMD model is discussed by using Pontryagin maximum principle and numerical method.First,the relative risk（RR）of HFMD infection increased with increasing tem-perature.With the relative humidity increase,the risk of infection RR increased and decreased.The propagation rateβ（t）is composed of temperature in exponential form,relative humidity in quadratic form,and school function in piecewise form.Secondly,the average basic reproduction number[R₀]are 1.9362 and 1.5478,respectively,indi-cating that HFMD would continue to be prevalent in Shanghai.Thirdly,temperature,relative humidity,and school opening all had explanatory effects on the outbreak of HFMD in Shanghai.Still,the temperature had the most vital explanatory power,followed by school holidays and relative humidity.Finally,the solution to the optimal control problem of our model of HFMD exists and is unique.Numerical simulation shows that the outbreak of HFMD will be effectively alleviated under ideal conditions.We obtain three conclusions about the prevention and control of HFMD.1)Ac-cording to the temperature,relative humidity and school start time,the outbreak peak of HFMD should be warned and targeted prevention and control measures should be taken.2)Reduce high indoor temperature when more than 31.5℃,and increase low relative humidity when less than 77.5%by opening the window for ventilation,adding houseplants,using air conditioners and humidifiers,reducing the incidence of HFMD and the number of infections.3)The risk of HFMD transmission during win-ter vacations is higher than during summer vacations.It is necessary to strengthen the publicity of HFMD prevention knowledge before winter vacations and strengthen the disinfection control measures during winter vacations in children’s hospitals,school classrooms,and other places where children gather to reduce the frequency of staff turnover during winter vacations.