Modeling And Analysing Of Disease Spreading Based On Time-Varying Network

The research on the propagation dynamics of infectious diseases on complex networks has been a hot point in academic research.Building mathematical models has become a common method for researches due to the inability to conduct in vivo experiments for disease transmission.Although the classical disease transmission models have achieved certain achievements in simulating the process of virus transmission,the assumptions they made in these models tend to lack of considering the various of process when the virus spreading in the different regions.Such as the fixed infection and curation rates.Moreover,the accuracy of existing epidemic models' predictions of the virus propagation trends also needs to be improved.However,one of the most important reason may be the lack of effective tools to see the trends in the change of infection rate over time of a particular virus at this stage.Therefore,the dissertation looked into the prediction of virus propagation trends based on the relevant theories,and checked it by the real data.Here are the main contents we have studied:(1)By analyzing the existing epidemic models and considering more practical factors,we construct virus propagation mathematical models based on time-varying network.These models use the individual-based mean-field method(IBMF)to discuss changes in the infection probability of nodes in discrete time under the conditions of variable virus infection and curation rates.Among these models,the transfer-rate epidemiological model focuses on the phenomenon of different contact patterns between biological individuals in the real network.Then,a weighted network is used in the transfer-rate epidemiological model.What's more,we make the weights in the network change over time.As for the activity propagation model,we take the impact of individual activity on the infection probability into account.(2)The algorithm for solving the mathematical model of the differential equation of virus propagation dynamics established in(1)is designed and implemented.In the simulation experiments,we use the data of H1N1,H3 and B-Yamagata viruses provided by the World Health Organization(WHO)in 2007-2016,2009-2016,and 2014-2017.According to the simulation experiments,we estimate the values of the parameters in the mathematical models,and the trends of infection rate in actual propagation.What's more,the time differences between the trends of infection rate and the trends of virus diffusion are also estimated.(3)In order to validate and apply the model,we assure the value of parameters in the influenza transmission case based on the actual data of influenza virus transmission.Then with using the model proposed in(1),we describe the propagation trend accurately and effectively predicts the spread of the virus in the next year.The main idea is to solve the mathematical model proposed by using computer simulation with the historical data provided by the World Health Organization(WHO).In this solution process,we find the trends of infection rate.Then the historical average of infection rate is used to be the value of infection rate in the next year for prediction.Then the results of simulation are compared with the real diffusion data.The comparison results show that the two trends are basically consistent.The main results of our study are: firstly,we constructe a virus propagation mathematical model on time-varying network with considering a variety of realistic factors.And the numerical solution algorithm to solve the propagation differential equation group model was proposed and implemented.To fulfill it,we find the trend of virus' infection rate in actual diffusion process,filling the gap in this direction.Secondly,with the actual transmission data provided by WHO,an accurate prediction of the spread of virus in the coming year is made according to the formula of the model and the simulation.In addition,the ideas of the research can be widely applied for the mathematical models in our research can be replaced by other models.The epidemic model proposed in the research not only can be applied to many fields other than biology virus propagation,for example,computer viruses,public opinion communication,social networks and so on,but also shed a new light on the modeling work in these fields.At the same time,our study can also provide staff in related fields with the trends of transmission rate of specific substances,and help predict the spread of substances in the future.Last but not least,the epidemic model has been proposed in the thesis provided a scientific approach to the controllability of the real time systems in efficiently.