Modeling And Analyses Of Several Kinds Of Influenza Model With The Effect Of Multi-factors Based On Data Driven

The outbreak of influenza is affected by a variety of factors,but how these factors affect the dynamic spread of influenza needs further researches.We mainly propose several kinds of influenza model with the effect of multi-factors in this paper.We study the dynamical behaviors of the model.First,we estimate the parameters of the model in combination with actual data.Next,the sensitivity and uncertainty of the main parameters of the model are explored.In addition,some reasonable preventions and control measures are given.The main works of this paper are as follows:In Chapter 1,we not only introduce the background and current research status of in-fluenza,but also give the theoretical knowledge related to this paper.In Chapter 2,we study the impact of Twitter on influenza.Twitter can play an important role in the control of influenza epidemics.Statistically significant correlations between the number of the percentage of tweets that are self-reported flu and the number of reported influenza cases are shown from Pearson correlation and cross-correlation analyses during the 2009 H1N1 flu outbreak in UK.A new H1N1 model with relapse which involves impact of Twitter is also proposed.Stabilities of all the equilibria of our model are obtained.The occurrence of backward and forward bifurcation is also established.The best-fit parameter values in our model are identified by grey wolf optimizer and nonlinear least square method from the data above.For determining key parameters during the outbreak of the disease with Twitter impact,the uncertainty and sensitivity analyses are explored by using a Latin hypercube sampling?LHS?method and evaluating the partial rank correlation coefficient?PRCC?.Our results show that Twitter reports have important implications for the control of infectious diseases.In Chapter 3,we study the effects of meteorological factors and unreported cases on seasonal influenza in Gansu Province.Influenza usually breaks out seasonally in temperate regions,especially in winter,infection rates and mortality rates of influenza increase signif-icantly,which means that dry air and cold temperatures accelerate the spread of influenza viruses.During the epidemic of infectious diseases,the neglect of unreported cases lead-s to an under-estimation of infection rates and basic reproduction number.In this chapter,we propose a new non-autonomous periodic differential equation model with meteorological factors by including unreported cases.First,the basic reproduction number is obtained and the global asymptotic stability of the disease-free periodic solution is proved.Furthermore,the existence of periodic solutions and the uniformly persistence of the model are demon-strated.Second,the best-fit parameter values in our model are identified by the MCMC algorithm from the collected data.We also estimate that the basic reproduction number is1.2288?95%CI:?1.2271,1.2305??.Then,to determine the key parameters of the model,uncertainty and sensitivity analyses are explored.Finally,our results show that influenza is more likely to spread in low Temperature,low Humidity and low Precipitation environments.Temperature is a more important factor than Relative Humidity and Precipitation during the influenza epidemic.In Chapter 4,we study the dynamic effects of ozone concentration in the air and pulse vaccination on seasonal influenza in Gansu Province.Common air pollutants,such as ozone?O₃?,sulfur dioxide?SO₂?,monoxide Nitrogen?NO?,nitrogen dioxide?NO₂?and particulate matter also affect the spread of influenza.In this chapter,we propose a non-autonomous im-pulsive differential equation model with the effects of ozone and vaccination.First,the basic regeneration number of the impulsive system is obtained,and the global asymptotic stability of the disease-free periodic solution is proved.Furthermore,the uniformly persistence of the system is demonstrated.Second,the unknown parameters of the ozone dynamics model are obtained by fitting the ozone concentration data by the least square method and Bootstrap.The MCMC algorithm is used to fit influenza data in Gansu Province to identify the most suitable parameter values of the system.The basic reproduction number R₀ is estimated to be 1.1487?95%CI:?1.1422,1.1551??.Then,a sensitivity analysis is performed on the system parameters.Finally,our results show that increasing the vaccination rate and appro-priately increasing the ozone concentration can effectively prevent and control the spread of influenza.