In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;...In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">fective</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algorithm is then employed for its inference. We then analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities.</span></span></span><span><span><span style="font-family:""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The adequacies of the three models to the final size data are examined. The four and three-dimensional models are found to outperform the two dimensional model on misclassified final size data.展开更多
In this paper,an extended heterogeneous SIR model is proposed,which generalizes the heterogeneous mean-field theory.Different from the traditional heterogeneous mean-field model only taking into account the heterogene...In this paper,an extended heterogeneous SIR model is proposed,which generalizes the heterogeneous mean-field theory.Different from the traditional heterogeneous mean-field model only taking into account the heterogeneity of degree,our model considers not only the heterogeneity of degree but also the heterogeneity of susceptibility and recovery rates.Then,we analytically study the basic reproductive number and the final epidemic size.Combining with numerical simulations,it is found that the basic reproductive number depends on the mean of distributions of susceptibility and disease course when both of them are independent.If the mean of these two distributions is identical,increasing the variance of susceptibility may block the spread of epidemics,while the corresponding increase in the variance of disease course has little effect on the final epidemic size.It is also shown that positive correlations between individual susceptibility,course of disease and the square of degree make the population more vulnerable to epidemic and avail to the epidemic prevalence,whereas the negative correlations make the population less vulnerable and impede the epidemic prevalence.展开更多
In this paper, a periodic seasonal influenza SVEIRL model is constructed to explore the mechanismby which seasonal influenza factors exert social impacts. Through dynamic analysis of the model andverification via nume...In this paper, a periodic seasonal influenza SVEIRL model is constructed to explore the mechanismby which seasonal influenza factors exert social impacts. Through dynamic analysis of the model andverification via numerical simulations, it is revealed that seasonal factors exhibit a significant positivecorrelation with both the basic reproduction number and the final epidemic scale. Using surveillance data frominstitutions including the Chinese National Influenza Center and the Public Health Science, the model isapplied to simulate the trends of influenza epidemic in China. Under multi-dimensional scenarios that includedifferent years, provinces, influenza subtypes, and the proportion of influenza-like cases in northern andsouthern regions of China, approximate values of seasonal factors for each scenario are calculated usingmethods such as genetic algorithms and parameter fitting. The findings reaffirm that the intensity of seasonalfactors is positively correlated with the scale of influenza epidemics.展开更多
文摘In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">fective</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algorithm is then employed for its inference. We then analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities.</span></span></span><span><span><span style="font-family:""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The adequacies of the three models to the final size data are examined. The four and three-dimensional models are found to outperform the two dimensional model on misclassified final size data.
基金This work is supported by the National Natural Science Foundation of China under Grant No.11331009The Science and Technology Innovation Team in Shanxi Province No.201605D131044-06。
文摘In this paper,an extended heterogeneous SIR model is proposed,which generalizes the heterogeneous mean-field theory.Different from the traditional heterogeneous mean-field model only taking into account the heterogeneity of degree,our model considers not only the heterogeneity of degree but also the heterogeneity of susceptibility and recovery rates.Then,we analytically study the basic reproductive number and the final epidemic size.Combining with numerical simulations,it is found that the basic reproductive number depends on the mean of distributions of susceptibility and disease course when both of them are independent.If the mean of these two distributions is identical,increasing the variance of susceptibility may block the spread of epidemics,while the corresponding increase in the variance of disease course has little effect on the final epidemic size.It is also shown that positive correlations between individual susceptibility,course of disease and the square of degree make the population more vulnerable to epidemic and avail to the epidemic prevalence,whereas the negative correlations make the population less vulnerable and impede the epidemic prevalence.
文摘In this paper, a periodic seasonal influenza SVEIRL model is constructed to explore the mechanismby which seasonal influenza factors exert social impacts. Through dynamic analysis of the model andverification via numerical simulations, it is revealed that seasonal factors exhibit a significant positivecorrelation with both the basic reproduction number and the final epidemic scale. Using surveillance data frominstitutions including the Chinese National Influenza Center and the Public Health Science, the model isapplied to simulate the trends of influenza epidemic in China. Under multi-dimensional scenarios that includedifferent years, provinces, influenza subtypes, and the proportion of influenza-like cases in northern andsouthern regions of China, approximate values of seasonal factors for each scenario are calculated usingmethods such as genetic algorithms and parameter fitting. The findings reaffirm that the intensity of seasonalfactors is positively correlated with the scale of influenza epidemics.
