Research On Treatment Threshold In Infectious Disease Model Based On Pair Approximation

The spread of infectious diseases can pose a threat to people’s life and the development of society.When infectious diseases are prevalent,how to effectively control their spread and eliminate infectious diseases as soon as possible is very important.There have been many theoretical researches on infectious diseases in the past,but the uneven distribution of medical resources caused by unbalanced regional development has been considered rarely.Therefore,how to effectively allocate medical resources to control the outbreak of infectious diseases is a very meaningful research topic.By means of mean field approximation and pair approximation method,SIS,SIR and SEIR models are established respectively considering birth and death of population.Numerical simulation was used to study the influence of infectivity,lethality,exposure rate,onset rate,treatment initiation time,abundance of medical resources and spatial concentration on treatment threshold.Among them,the treatment threshold refers to the minimum medical resources required for effective control of infectious diseases.The main research results are as follows:When infectious diseases occur,the earlier the start time of treatment is,the lower the infectivity of infectious diseases is,the lower the contact rate is,the lower the rate of onset is,the lower the threshold of treatment is,and these factors are proportional to the threshold of treatment.But the higher the fatality rate of an infectious disease is,the lower the threshold for treatment is.This indicates that early surveillance of infectious diseases,"early detection and early treatment",and control of the contact rate of infected patients can effectively reduce the threshold of treatment.In addition,when the medical resources are limited,the dispersive distribution of resources can also reduce the treatment threshold slightly.Three pairs approximation models were compared,and it was found that the treatment threshold of SEIR-PA model was lower than that of SIR-PA model when the treatment started earlier,the infectivity smaller,the contact rate smaller and the lethality larger.When the start time of treatment,infectivity and contact rate gradually increase or the lethality gradually decreases,the treatment threshold of SEIR-PA model will gradually exceed that of SIR-PA model.Moreover,these factors have the greatest influence on SEIR-PA model.From the results we know that infectious diseases with different characteristics have different demands on the amount of medical resources;When the medical resources are limited,the diversification strategy can effectively prevent a run on medical resources.The results have a certain guiding significance for the control of infectious diseases.