The Application Of Epidemic Dynamics Modeling In Varicella Forecasting And Control Measures Effect Evaluating

Infectious diseases are still regarded as the main burdens around the world, especially in developing countries. Epidemic dynamics is an important quantitative analysis method to study on infectious diseases. In consideration of ethics, study on transmission of the infectious diseases can't conduct in population experiment way. So, mathematical modeling plays an irreplaceable role to study the characteristic of spreading and effect evaluation of intervention measures.Varicella is an acute and highly contagious respiratory disease caused by varicella-zoster virus (VZV). Most people have been infected VZV in childhood, and it frequently leads to outbreak in primary school or kindergarten. Varicella is not notifiable disease and still lacks of systematic and complete epidemic data in China. In the present work, we apply epidemic dynamics modeling theory and method to forecast the epidemic trend and to evaluate the effect of intervention measures.Objectives1. Epidemic trend forecasting:by fitting an outbreak event, to predict the future course of the epidemic; and considering more complicated factors such as population change, seasonal characteristics and herpes zoster prevalence, to discuss the long term epidemic trend. 2. Effect of intervention measures evaluating:by adding the intervention measures in the model, to evaluate the hypothetical effects of cases isolation, emergent vaccination in outbreak and the long term impact of immunization program.3. Model expressing:to explore how to implement the model easily by public health workers.Materials and Methods1. MaterialsThe varicella outbreak data from a field research report which took place in a primary school in Zhejiang province in 2006. The national-wide varicella epidemic data from an analysis report that derived from National Diseases Reporting System. The population levels of VZV antibody resulted from combining the serum test reports in Hangzhou, Shanghai and Guangzhou in the same period. And, the demographic data based on 1% national population sampling survey in 2005 which public informed by National Bureau of Statistics of China.2. Methods1) A discrete time delay SEIR model for varicella outbreak prevalence forecasting and control measures effect evaluatingThe model was discretized on a SEIR continuous model. The time delay effect of latent period and infectious period was took into account as well. The number of expected cases could be obtained by fitting the model; and the control measures effect could be evaluated by comparing the different number of cases in a given scenario. The model was carried out in EXCEL2003.2) An age-structured model for long term varicella trend forecasting and immunization impact evaluatingAdding maternal immunity class and herpes zoster infected class in the SEIR model, and dividing the whole population into 7 age groups that with different force of infect coefficient to forecast the long term varicella trend. In addition, the model included influence factors such as birth, aging and naturally death in the population. The vaccine effect and other impacts were discussed by comparing the long term results of different immunization program. The numeric simulation was executed by STELLA9.Results1. Varicella outbreak prevalence forecasting and control measures effect evaluating A discrete time delay SEIR model was used to fit a varicella outbreak which took place in a primary school. The total number of students was 1671, and the estimated number of the susceptible was 514 in the initial stage of the outbreak. In the scenario that without any control measures, most of the susceptible will be infected, and the number of expected cases is 504 with an attack rate of 30.76%. The course of the epidemic lasts for 4 months and the peak epidemic time is 78 days after the onset of index case. 'Generation'phenomenon has been observed in the course of the epidemic with the interval of two weeks. With the perfect cases isolation in the early stage of an outbreak, epidemic spreading can be disrupted effectively. However, as with the communicability in the late stage of incubation period, VZV spreading can't be blocked utterly under the intervention only focussing on the patients. The effect of emergent vaccination with high coverage rate in the early stage is better than the perfect cases isolation under the same conditions. For reasons of controlling the outbreak effectively, it's suggested that the coverage rate should reach to 90%.2. Long term varicella epidemic trend forecasting and immunization impact evaluating The long term (80 years) simulation results indicate that varicella incidence is fluctuated dramatically in the first 5 years, and then keep steadily in the later course with the incidence rate around 8.3%o per year. Herpes zoster incidence keeps steadily all the time with the incidence rate around 2.2%o per year. By comparison, the incidence of 4-age group is much higher than others'with the incidence rate up to 65%o per year in the late of simulation period. With the routine immunization program only inoculating the one year old children, the vaccine effect will emerge gradually and keep stable 10 years later. The effect has the positive relationship with the coverage rate. When the coverage rate is 10%,30%,50%, 70% or 90%, the yearly varicella incidence rate is dropped 11%,34%,57%,78% and 92%, respectively. Under the same coverage rate, inoculating younger children will gain more benefits. When the coverage rate is 90%, inoculating 7-,4-, or 1-year old age group, the yearly varicella incidence rate is dropped 82%,90%, and 92%, respectively. With the higher coverage rate of vaccine, the proportion of breakthrough cases will increase correspondingly. Immunization program will increase the average age of varicella infection, nevertheless, the varicella cases in elder groups are reduced as well. Sensitivity analysis indicates that whether the herpes zoster cases have the ability to spread the virus will have great influence on varicella epidemic trend. Ignoring the communicability of herpes zoster cases, the varicella epidemic turns out to have cyclicity phenomenon, and the interval of epidemic peaks is about 6-8 years. While taking into account its communicability, the varicella epidemic intensity will keep stable in whole course. Furthermore, the communicability of herpes zoster cases has greater influence on the vaccine effect. Ignoring its communicability, and inoculating the one year old children with the coverage rate of 90%, the varicella will die out after three years (the model ignoring the immigration of infection source). While taking into account its communicability, the varicella will exist persistently with the lower level incidence (the incident rate was around 0.7%o per year) under the same coverage rate.ConclusionA discrete time delay SEIR model was used to fit a varicella outbreak event. The number of expected cases can be regarded as the reference to evaluate the control measures effect. Both the effects of perfect cases isolation and emergent vaccination with high coverage rate in the initial stage of an outbreak are soundly. An age-structured model was used to forecast long term varicella trend. The results indicate that varicella epidemic doesn't have the cyclical phenomenon, and the incidence rate is around 8.3%o per year. It is suggested that the vaccine lacks of herd protection or it can only protect the individual who has been inoculated. Because VZV can establish in a latent form in the dorsal root ganglia after primary infection and will be reactivated after dozens years, varicella is unlikely to be eliminated by mass vaccination in short term.The theoretical and practical meanings of present work may list as follows:It provides one way to evaluate the effect of control measures in an outbreak event by comparing the number of expected cases with the number of actual cases. It's available to give advice to choose the effective field control measures by quantitatively comparing the effect of theoretical emergency measures. Even the lack of systemic and complete epidemic data nowadays, by comprehensive analyzing the simulation results, it's feasible to implement the long term varicella epidemic trend forecasting, the influence factors identifying and the public health utility of varicella vaccine judging. Besides, the conclusion of this work may offer helpful reference for further field research on VZV infection.