Analysis On The Mean First-passage Time Of Animal Diseases On Basis Of Patches Models

With the development of global economics, the circulation of humans, animals, andby-products is becoming more frequent, which results in more easily spread in the globe forsome unexpected human diseases, animal diseases and zoonosis. When research on theprevention and control of cross-regional epidemics is conducted, the mean first-passage of theinfectious and the susceptible, namely epidemic mean first-passage time, needs to beinvestigated. As for the researches about that mentioned above, most of works, by applyingstochastic methods and according to the initial propagation ways, calculate the generalexpression of epidemic first-passage time. The previous models built is mainly SI models,where individuals mix evenly, neglecting the heterogeneity among individuals. Study on thefirst-passage time is related to the migration among individuals, which singly depends ontraffic flow. Recently, dynamic models about migration is mainly patches models, most ofwhich are in light of human diseases. The individuals are homogeneously mixing and thespread approach relatively simplex. Hence, the main work of paper is in terms of thefirst-passage time of animal diseases.Chapter1, mainly introduces the research significance and the current state at home andabroad and the main content of paper.Chapter2, builds patches dynamic models for probing influence migration makes ondiseases propagation. The divided administrative regions are regarded as different patches.Considering that animal cultivation is chiefly characteristic of farms, we assume thatindividuals in patches is distributed into different farms seen as sub-patches and distancebetween sub-patches is different. The individuals in sub-patches are mingled evenly. Besidesindividual migration, the epidemic spread is also related to distance, based on which keythreshold is calculated and we do the quantitative and qualitative analysis. Finally, through numerical simulation the reasonability of models is demonstrated.Chapter3, based on the patches models in chapter two, analyzes in details sorts of spreadways in initial period of epidemics and gives the general expression of epidemic first-passagetime in different spread cases by applying stochastic methods. Furthermore, numericalexamples analyze the effects migration and distance take on first-passage time, which providetheoretical basis for the establishment of prevention and control measures.Chapter4, in terms of the cow brucellosis’ situation for7cities, Hangzhou, Ningbo, Jinhua,,Wenzhou, Taizhou, Huzhou, Quzhou in Zhejiang province of China, establishes patchesdynamic model and gives the first-passage time of the cow brucellosis for7cities. Theattained results bring theoretical foundations for the prevention of cow brucellosis in Zhejiang.