The impact of vaccine failure rate on epidemic dynamics in responsive networks.
An SIS model based on the microscopic Markov-chain approximation is considered in this paper. It is assumed that the individual vaccination behavior depends on the contact awareness, local and global information of an epidemic. To better simulate the real situation, the vaccine failure rate is also taken into consideration. Our main conclusions are given in the following. First, we show that if the vaccine failure rate α is zero, then the epidemic eventually dies out regardless of what the network structure is or how large the effective spreading rate and the immunization response rates of an epidemic are. Second, we show that for any positive α, there exists a positive epidemic threshold depending on an adjusted network structure, which is only determined by the structure of the original network, the positive vaccine failure rate and the immunization response rate for contact awareness. Moreover, the epidemic threshold increases with respect to the strength of the immunization response rate for contact awareness. Finally, if the vaccine failure rate and the immunization response rate for contact awareness are positive, then there exists a critical vaccine failure rate αc > 0 so that the disease free equilibrium (DFE) is stable (resp., unstable) if α < αc (resp., α > αc). Numerical simulations to see the effectiveness of our theoretical results are also provided.
Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan.
Yu-Hao
YH
Liang
Department of Applied Mathematics, and Center of Mathematics Modeling and Scientific Computing, National Chiao Tung University, Hsinchu, Taiwan.
Jonq
J
Juang
D000465:Algorithms; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D058872:Epidemics; D006801:Humans; D007114:Immunization / Q000379:methods*; D008390:Markov Chains; D008954:Models, Biological; D012944:Social Support; D017211:Treatment Failure; D014612:Vaccines
D014612:Vaccines