SIR Model And Its Application In Measles Outbreak

Measles,an acute respiratory infection caused by the measles virus,spreads rapidly and is highly infectious.Before the introduction of the vaccine in 1963,major epidemics occurred every 2-3 years and most infected people are young children.After introduction of the measles vaccine and universal vaccination of young children,the incidence of measles in children is gradually reduced.How-ever,the antibody produced by the vaccine gradually disappears over time and the onset age of measles begins to shift.This paper takes adult measles patients as the object to study and explores the coping strategies for adult measles.In this paper,when modelling the data of adult patients,the SIR model is used.In the section of related theories,with the help of forward Kolmogorov equations and probability generating function,the conclusion that deterministic model is the mean process of stochastic model when the covariance terms are neglected is proved.In the section of empirical research,according to the characteristics of measles,we fix the recovery parameter first.Then the original data could be converted to the number of daily infectives which is required by SIR model.At last,the infection parameter and the number of initial susceptibles are estimated with the aid of the method of LSE.When estimating parameters in stochastic model,1000 paths are generated and we calculate the mean of 1000 paths as the fitting data.In the section of assessment of the outbreak,this paper first compares the stochastic model with the deterministic model and concludes that the stochastic model is better.Under the frame of stochastic model,the outbreak is discussed from three aspects of isolating infectives,cutting off the transmission route and protecting the susceptibles.By changing the corresponding parameters,we draw pictures about the influence of taking measures.Finally,the study shows that the injection of measles vaccines is the most effec-tive measure to suppress the measles epidemic,which is consistent with people’s impression of the measles epidemic.Although the effect of cutting off the trans-mission route is limited,the effect is still obvious when the infection parameter is reduced by 30%.Therefore,the main way to avoid the occurrence of measles outbreak is increasing the rate of coverage of measles vaccine for adults while popularizing the vaccine for young children.Only in this way can we effectively reduce the annual incidence of measles and minimize the impact of measles on people’s live.