The Establishment And Simulation Of Echinococcosis Model In Xinjiang

Objective: Construct the echinococcosis dynamic model with Xinjiang local characteristics to discuss the feasibility of various mathematical models in echinococcosis research and application in Xinjiang. Study the overall incidence of echinococcosis in Xinjiang, reveal the rules of propagation, prevalence and development of echinococcosis, predict the prevalence trend of this disease in the future, simulate the key factors affecting the prevalence of echinococcosis, which will provide powerful theoretical and quantity basis for the prevention, control and decision-making of echinococcosis in Xinjiang. Methods: Firstly, the ARIMA prediction model was applied to predict the overall incidence of echinococcosis in Xinjiang according to the clinical characters of this disease. A relatively optimal ARIMA prediction model can be built through several modeling process, such as sequence tranquilization, pattern recognition, parameter estimation and model diagnostic. The incidence data of echinococcosis in Xinjiang of each month from 2004 to 2012 was used for fitting model and predicting the overall prevalence in the short period. Secondly, two kinds of dynamics models of echinococcosis transmission, the discrete and continuous dynamics model, were constructed from macroscopic and microscopic perspective according to dynamics theory of infectious disease and transmission mechanism of echinococcosis. And the kinetic properties of the two dynamics models above, such as threshold condition, disease-free equilibrium and endemic equilibrium, were also studied. Thirdly, the parameters of the two models were estimated and the approximate values of basic reproductive number for the spread of echincoccsis were calculated based on the incidence data of echincoccsis report of Xinjiang and Urumqi in recent years. According to the above steps, the prevalence of echinococcosis can be predicted from the long-term trends in the future. And the critical factors effecting the prevalence of echinococcosis can be achieved by analyzing the sensitivity of the model parameters. Results: Firstly, the stationarity test was implemented on the incidence data of each month of echinococcosis in Xinjiang. Experimental results showed that the sequence is a non-stationary time series. The ARIMA prediction model of echinococcosis was constructed based on the logarithm and first-order difference operation of the original sequence. The ARIMA(1, 1, 0) was determined to be the optimal prediction model for Xinjiang echinococcosis through several modeling process, such as pattern recognition, parameter estimation and model diagnostic. Prediction results show that the cumulative incidence of echinococcosis in 2013 has an increase of 592 cases compared with 2012. Secondly, the discrete dynamics model of echinococcosis was constructed from the microscopic perspective. Experimental result shows that R0=1.36>1. According to the threshold theory of dynamics, the number of cases of echinococcosis in Xinjiang presents a trend of growth in a short term when keep the existing control measures unchanged. The prediction results indicated that the incidence data of echinococcosis in Xinjiang can reach the highest number of 900 cases in 2024. And after that the number of incidence begins to gradually decline and tend to be stable. Quantitative simulation of the key factors that influence the spread of echinococcosis, such as dogs’ infection rates β1, recovery rates σ, the new increased numbers of dogs A1 and dogs’ mortality rate d1. And the dogs’ infection rates β1outperforms to other factors. In addition, the continuous dynamics model of echinococcosis was constructed from the macroscopic perspective. The two parameters of the model, mean absolute error percentage and root mean square error percentage, are 3.36 and 4.42, respectively. Both of them are less than 10%, which indicates that continuous model of echinococcosis is reliable and reasonable for studying the epidemic condition of echinococcosis in Urumqi. Experimental result shows that R0=1.129>1. According to the threshold theory, the number of cases of echinococcosis in Urumqi presents a tendency of increasing when keep the existing control measures unchanged. The results of sensitivity analysis illustrate that dogs’ transmission rate has the largest effect on R0(∣PRCC∣=0.9732) and the following is dogs’ recovery rate σ(∣PRCC∣=0.8706). Conclusion: Using the two methods of ARIMA model and dynamics model of infectious diseases to quantitatively analyze and predict prevalent condition of echinococcosis in Xinjiang is feasible. The experimental results show that the incidence of echinococcosis in Xinjiang is in the trend of growth, and reveal that the key to control echinococcosis is to control the definitive host of infection dogs and strengthen the management of dogs.