The Effect Of Population Heterogeneity On The Final Size Of Multi-group Model

The heterogeneity of population has an important impact on the basic reproduction number and the final size of the infectious diseases.In this paper,we study two types of infectious disease with population heterogeneity: acute hemorrhagic conjunctivitis and influenza H1N1,and establish the heterogeneous grouped model to calculate the basic reproduction number and the final size.The effectiveness of infectious disease prevention and control strategy was evaluated by numerical simulation.The main contributions of this paper are as follows:First part,when the population is homogeneous,i.e.a group model,the final size increases with the increase of the basic reproduction number.In order to discuss the relationship between the both when the population is heterogeneous,we establish a multi-group SIR model to calculate the basic reproduction number and the final size of the model.When the population mixing is proportional and preferential,the influence of changing parameters(activity,preferential contact ratio,contact rate,etc.)on the final size may not increase with the increase of the basic reproduction number.Second part,in order to estimate the final size of the outbreak of acute hemorrhagic conjunctivitis on campus,a grouped SIR model was established by taking an outbreak of acute hemorrhagic conjunctivitis in a school in Changsha in 2011 as an example.The population was divided into those with better hygienic habits and with worse hygienic habits,and the basic reproduction number and final size of the model were obtained.The numerical simulation shows that when the proportion of the two groups is 10:1,the final size decreases by 84%.Third part,to explore the influence of wearing masks on the transmission of influenza H1N1,a grouped SEIAR model was established with N95 masks as an example.One group was the people without masks,the other group was the people with masks.The basic reproduction number is obtained by using the method of next generation matrix.When 10%,25%,50% of the population wore masks,the final size was reduced by 16%,27% and 34%respectively.