Numerical Solution For Two Kinds Of Epidemic Models And Its Parameter Identification

Epidemic model is always one of the important research object in computation mathematics and applied mathematics.Especially,it is more meaningful to study the mathematics theory of the epidemic model under the global Pandemic of 2019 Novel Coronavirus.The numerical computation method and parameter identification algorithm for two kinds of modified SIR(Susceptible-Infectious-Recovered)epidemic models are considered in this paper.The first modified SIR epidemic model is called SIRD(Susceptible-Infectious-Recovered-Death)model,which reflects the death numbers different from the classic SIR model.The modified SIRD epidemic model is an nonlinear differentiation equations coupled model with four variables.As to this model,the existence and uniqueness theorem for the simultaneous identification of the three parameters,i.e.,infection rate,curing rate and death rate,is proven with the terminal observation data.Neural network is proposed to solve the simultaneous identification.The inversion algorithm is tested feasibly by numerical example.The second modified SIR epidemic model is relative to the spatial variables,which is more practical to the real live.In application,the cases or the density of the infected populations are different between different places,so the model relative to the spatial variables is more reasonable.For simplification,the two dimensional case is only considered.Numerically,three different finite element schemes are proposed,and the corresponding numerical analysis,including the stability analysis,convergence analysis,and the existence with the boundedness of the solution for the discrete finite element algebra system is considered.From the view of application,inversion algorithm for the infection rate parameter is proposed based on the optimal perturbation method.The inversion algorithm is versified by several numerical examples.