Dynamics Of Preschoolers Epidemic Model Influenced By Off-class Education And Optimal Control

According to the survey,the children health examination is serious and strict in the kindergarten,so the disease transmission probability in the kindergarten is relatively small,but in off-class education institutions children health check relatively lax perfunctory,the disease transmission probability is higher.Therefore,according to the different transmission mechanisms of infectious diseases in school and off school,we establish and study a preschoolers disease model with the influence of off-class education.The model is analyzed by the qualitative analysis and the basic reproduction number of the disease is obtained.The analysis results of the model show that,when the basic reproduction number₀R（27）1,the disease-free equilibrium is globally asymptotically stable;when the basic reproduction numberR₀（29）1 and the disease equilibrium point is globally asymptotically stable when certain conditions are met,the endemic equilibrium is globally asymptotically stable.The numerical results show that proper adjustment of off-class education can effectively control the spread of infectious diseases in preschoolers.The contact number of off-class education has a great influence on the basic reproduction number.Proper control and supervision of off-class education can effectively control the spread of disease among children during the epidemic period.The optimal control model with the influence of off-class education is built by considering personal protection,the disease treatment,the spraying disinfectant in the environment.The optimal control strategies are analyzed by Pontryagin’s maximum principle.The optimal control functions are simulated numerically by the forward-sweep method.The simulation results show that three optimal control strategies will reduce the proportion of the infected population and the exposed population.In addition,the optimal control strategies depend on parameters,that is,parameter changes in the system will also lead to the changes in the optimal strategies.Our results show that the effect of off-class education on the transmission of children diseases should not be ignored.This study provides some theoretical basis and control strategy for economic and effective control of disease transmission in preschoolers,which can reduce a certain burden for the families of preschoolers and save effective medical resources for the society.