Sveir epidemiological model with varying infectivity and distributed delays - Jinliang Wang; Gang Huang; Yasuhiro Takeuchi; Shengqiang Liu (Mathematical Biosciences and Engineering)
In this paper, based on an SEIR epidemiologicalmodel with distributed delays to account for varying infectivity, weintroduce a vaccination compartment, leading to an SVEIR model. Byemploying direct Lyapunov method and LaSalle's invariance principle,we construct appropriate functionals that integrate over past statesto establish global asymptotic stability conditions, which arecompletely determined by the basic reproduction number$\mathcal{R}_0^V$. More precisely, it is shown that, if$\mathcal{R}_0^V≤ 1$, then the disease free equilibrium isglobally asymptotically stable; if $\mathcal{R}_0^V> 1$, then there exists a unique endemic equilibrium which isglobally asymptotically stable. Mathematicalresults suggest that vaccination is helpful for disease control bydecreasing the basic reproduction number. However, there is anecessary condition for successful elimination of disease. If thetime for the vaccinees to obtain immunity or the possibility forthem to be infected before acquiring immunity can be neglected, thiscondition would be satisfied and the disease can always be eradicatedby some suitable vaccination strategies. This may lead toover-evaluating the effect of vaccination.