Optimal vaccination strategy for a mean-field stochastic susceptible-infected-vaccinated system

The parameters of biological system may change under the influence of different states or state processes.The change of parameters can also affect the dynamic behaviors of epidemic disease.This paper presents a mean field stochastic susceptible-infectedvaccinated(SIV)epidemic model which parameters depend on the state process.The sufficient and necessary conditions of optimal control of the novel epidemic model are obtained by maximum principle.Finally,we perform representative numerical simulations to illustrate the theoretical results and further discuss the feasibility based on the hand,foot and mouth disease(HFMD)data in China.

Dynamics of a stochastic delayed avian influenza model with mutation and temporary immunity

In this paper,the dynamic behaviors are studied for a stochastic delayed avian influenza model with mutation and temporary immunity.First,we prove the existence and uniqueness of the global positive solution for the stochastic model.Second,we give two different thresholds R_(01)^(s) and,R_(02)^(s) and further establish the sufficient conditions of extinction and persistence in the mean for the avian-only subsystem and avian-human system,respectively.Compared with the corresponding deterministic model,the thresholds affected by the white noises are smaller than the ones of the deterministic system.Finally,numerical simulations are carried out to support our theoretical results.It is concluded that the vaccination immunity period can suppress the spread of avian influenza during poultry and human populations,while prompt the spread of mutant avian influenza in human population.