Dynamic Modelling And Analysis Of Emerging Infectious Diseases

This thesis mainly researches the spread of emerging infectious diseases taking COVID-19 as an example.A epidemic model where the total population size consists of five compartments including the susceptible,the exposed,the asymptomatic,the infected and the removed is investigated firstly,which is theoretically analyzed in continuous-time compartmental version and discrete-time version on complex networks.Based on Jury criterion,Routh-Hurwitz criterion and LaSalle invariant set principle,if σm>αmγ+σβ holds,there is only a globally stable disease-free equilibrium point in continuous model.Otherwise,there are two equilibrium points where the diseasefree one is unstable and the endemic one is globally and asymptotically stable.Besides,the threshold condition σm=k(αmγ+σβ)which determines whether disease can emerge or not is given on discrete-time version,and the local and global stability of two kinds of equilibrium points are obtained on complex networks which hold when epidemic is weak(α<<1,β<<1).Then we establish a class of delayed epidemic model with temporary quarantine by augmenting with the quarantine state.A stochastic model is further given when the fluctuation is introduced into the whole system.By using It? formula and Lyapunov methods,we show that this system admits a unique global positive solution with any positive initial value.Sufficient conditions for extinction and persistence of disease are also obtained.Under the condition μ>1/4(σ12∨σ22∨σ32∨σ42),the disease eventually becomes extinct with negative exponential rate when R0<1,and weak permanence and persistence in the mean are obtained respectively when R0>1,which implies that the disease will prevail in a long run.Consequently,a number of illustrative examples can be used to verify main theoretical conclusions which are separately carried out with numerical simulations.