Prediction,Early Warning And Evaluation Of Influenza Transmission Capacity:Based On Mathematical Model

Objective:Understand and master the epidemic characteristics and distribution of influenza,predict the trend of influenza;Explore the inflection point of influenza epidemic speed change,infer the"early warning week"of influenza to implement early prevention and control intervention;Quantify and evaluate the transmission capacity of different types of influenza and evaluate the effect of influenza vaccination,to provide scientific basis for improving the level of influenza prevention and control in China.Methods:This study was divided into three parts.（1）The data of influenza was been obtained in China from 2010 to 2019,the epidemic dynamics,hot strains,time distribution of influenza were been analyzed,ARIMA time series model was used to predict the trend of influenza.（2）According to the periodicity of influenza,the logistic differential equation was used to deduce the"epidemic acceleration week"and"suggested early warning week"of influenza,then a complete cycle was selected and compared with the actual value to evaluate the fitting effect of the model.（3）According to the characteristics of influenza incidence and transmission law,the SEIABR transmission dynamics model was established.The model parameters were obtained by consulting relevant literature,statistical yearbook and fitting with actual data,and the influenza transmission probability（β）was fitted and estimated with the tools of 1stop,Matlab7.1 and Berkeley Madonna 8.3.18 to compare the transmission capacity of different types of influenza.At the same time,based on the original seiabr model,the duration of a single influenza cycle and the cumulative number of patients were simulated with different vaccination rates to evaluate the effect of vaccination.Results:（1）In 2010-2019 years,671693 cases of influenza were reported in China,the average incidence rate was 4.90/million,and the incidence rate increased significantly after 2014,with an average speed of 111.72%;Among different types of influenza,influenza A accounted for 66.85%,while influenza B accounted for 33.15%,H3N2 accounted for the highest proportion（38.79%）,followed by H1N1（27.01%）;A total of 430791cases of Influenza（64.14%）were reported in December,January,February and March,influenza in Winter accounted for 49.28%of the annual incidence;Influenza A（H1N1）and Yamagata B（Yamagata）were mainly concentrated in December,January,February and March each year,Influenza A（H3N2）had a large number of cases in December,January,February,March and July,August,September,while influenza B（Victoria）was mainly concentrated in March and April every year.（2）The optimal model of all Influenza was ARIMA（1,2,1）（0,1,1）₁₂,the data information was fully extracted（Q=14.257,P=0.506>0.05）,the relative error of most monthly forecast values was controlled at about 10%;The optimal model of influenza A was ARIMA（2,1,1）（0,2,2）₁₂,and the data information was fully extracted（Q=13.236,P=0.430>0.05）,it was predicted that the incidence rate of influenza A in December,January,February and March would be higher,and dropped rapidly in April,which was similar to the actual situation,and the relative error of the prediction in most months was lower than 10%;The optimal model of influenza B was ARIMA（1,2,1）（1,0,1）₁₂,and the data information was extracted adequately（Q=9.841,P=0.774>0.05）,however,the relative error was higher in the remaining months except November and December.（3）The incidence of influenza was seasonal and cyclical,and there were two epidemic cycles every year,the epidemic cycle in summer and autumn was 11 weeks to 36 weeks and the epidemic cycle in winter and spring was 37 weeks to the 10th week of the next year;Logistic model had a good fitting effect with the influenza incidence period（z=-1.709,P=0.088>0.05）,the inflection point values of the early time of the epidemic changes of the influenza cycle,that is,the"epidemic acceleration week"was the（22±1.78）week and（46±1.46）week,and the"early warning week"of influenza were the 20th and 44th week of each year respectively.（4）The SEIABR model was established to simulate the annual influenza epidemic cycle,the spread probability（β）of influenza was（7.95±1.27）×10^-10,the transmission probability of influenza A and influenza B were（7.89±0.78）×10^-10and（5.88±0.97）×10^-10respectively,Influenza A（H1N1）has the strongest transmission ability,βwas（7.25±0.82）×10^-10.（5）The model showed that with the increase of vaccination rate,the duration,peak value and cumulative number of influenza cases decreased continuously.When the vaccination rate was 20%,it was closed to the actual situation in 2019,when the vaccination rate reached 60%,the number of patients decreased by 73.48%,when the vaccination rate reached 80%,the duration of influenza was only 40 days,and the cumulative number of patients was only 23.Conclusion:（1）The average incidence rate of influenza in China was4.90/million,which ranked first in the class C infectious diseases,and had increased significantly after 2014.Influenza A（H3N2）and H1N1 were the main types of influenza,while influenza B（Yamagata）and Victoria were prevalent alternately;The incidence of influenza was mainly concentrated in December,January,February and March,but the hot spot time of different subtypes of influenza were not completely consistent,targeted prevention and control should be implemented according to the hot spots of different subtypes of influenza.（2）ARIMA time series model could predict the trend of influenza and influenza A,but the relative error of prediction for influenza B was high,which may be related to there was no obvious long-term trend of influenza B.（3）According to the logistic differential equation,the"early warning week"of influenza in summer and autumn was recommended as the 20th week（May）of each year,focusing on the prevention and control of influenza A（H3N2）,and the"early warning week"of winter and spring influenza was the 44th week（October）to prevent and control the co-epidemic of various influenza strains.（4）According to SEIABR model,the average transmission probabilityβof influenza was（7.95±1.27）×10^-10,and the transmission capacity of influenza A was higher than that of influenza B,Influenza A（H1N1）has the strongest transmission ability.（5）Simulation of different vaccination rates on influenza prevention and control effect,with the increase of vaccination rate,influenza single cycle duration,peak and cumulative number of patients decreased.When the vaccination rate was20%,it was close to the actual situation in 2019;when the vaccination rate reached 60%,the epidemic situation was well controlled.It is suggested to improve the vaccination rate and complete the vaccination before the 42nd week（early October）of each year.