Application Of Space State Model In Modeling The Measles Epidemic

Background and objectiveMeasles is an acute infectious disease caused by measles virus infection.The sources of infection for measles are the measles patients.And the main route of transmission is the droplet infection.China promised the World Health Organization to eliminate measles in 2012,but for various reasons,the prevalence of measles nationwide still has an upward trend.Shandong Province has high population density and high mobility.Exploring the characteristics of measles epidemic in recent years still has important public health significance,according to the characteristics of measles.Common epidemiological research methods include observational studies and experimental studies,while the theoretical epidemiological methods are less studied.The conventional dynamics model of ordinary differential equations of infectious diseases has the characteristics of simple modeling and faster calculation.However,the estimated parameters of this method are the mean of the corresponding Markov chain,and cannot consider the effect of random factors on the number of morbidity.At the same time,the output curve of the ordinary differential equation model is smooth and the city with less data is not applicable.The Kalman filter is practical.But the Kalman filter is applied to the model that the incidence of data,noise and parameters need to meet the assumption of normality,so the method has some limitations.The space state model can assume that the data,noise,and parameters satisfy any distribution,which is a new method of theoretical epidemiological research.Due to the lack of specific research on vaccine protection rates in recent years and data such as vaccine efficiency,several hypotheses should be made for important uncertain parameters.The number of basic reproduction number(R0)which is the average second generation cases that a case can produce can measure the infectivity of measles.This study used the basic regeneration number to show the risk of measles outbreaks in different cities and calculated vaccine efficiency for the elimination of measles in Shandong province,and aimed to provide scientific guidance for the development of measles elimination in Shandong Province.A state space model of Shandong Province and its 17 cities were formulated based on the data of measles in 2014 and 2015,and calculated the number of basic reproduction number(R0)and the target vaccine protection rate of measles elimination.Scientific guidance is provided for policy formulation of measles elimination in Shandong Province.Data and methodsThe data for this study were collected from the direct reporting system of infectious diseases in Shandong Province from 2014 to 2015,including onset time and incidence location.Based on the time and place of measles,the appropriate state space model was established.The parameters were estimated by Iterated Filter.The confidence interval was estimated by profile likelihood function.According to the national standard for measles elimination,the measles elimination target was defined as a morbidity rate of less than one millionth.The probability of measles elimination was estimated by statistical simulation with different vaccine efficiency hypothesis.Results1.Basic reproduction number of Shandong Province during 2014?2015Basic reproduction number were 2.49(95%CI:2.45?2.55),2.61(95%CI:2.55?2.69),3.34(95%CI:3.29?3.48)and 5.07(95%CI:4.96?5.24)respectively under the assumption of true vaccine efficiency of 50%,60%,70%and 80%.2.Basic reproduction number of 17 cities in Shandong Province during 2014?2015The basic reproduction number of 17 cities are 4.20(Jining),4.12(Taian),3.93(Heze),3.92(Dezhou),3.81(Weifang),3.81(Laiwu),3.47(Yantai),3.45(Rizhao),3.42(Jinan),3.33(Dongying),3.27(Zaozhuang),3.21(Zibo),2.98(Binzhou),2.91(Weihai),2.87(Qingdao),2.39(Linyi)and 2.35(Liaocheng)respectively from high to low.3.The target vaccine efficacy of measles eliminationAssuming that the real world vaccine efficacy is 60%,if the vaccine efficacy is increased to 75%by vaccine immunization,the probability of measles elimination is 30.32%according to the simulation results,but if the vaccine efficacy is increased to 78.13%,the probability of measles elimination is 95.15%.If vaccine efficacy increased to 80.00%,measles elimination probability is 99.80%.Assuming that the real world vaccine efficacy is 70%,if the vaccine efficacy is increased to 81.55%by immunization measures,the probability of measles elimination is 95.30%.When the vaccine efficacy is 82.50%,the probability of elimination of measles is 99.22%.Conclusions1.The basic reproduction number shows that the measles transmission ability varies between different cities.The south and east of Shandong province is higher than north and west.2.If the real world vaccine efficacy is low,it means that more people in the crowd need immunization protection,and if the crowd vaccine immunization rate is high,the vaccine efficacy increased slightly.3.State space model with process model and observation model considering the measurement error is suitable for analysis the measles epidemic.