Infectious disease models with generalized nonlinear vaccination rate and temporary immunity

This paper incorporates generalized nonlinear vaccination rate and temporary immunity into the infectious disease models and presents the corresponding system. The qualitative results show that the disease-free equilibrium point and the endemic equilibrium point are globally asymptotically stable under some certain conditions. The local sensitivity analysis reveals that the importance of the critical parameters to the effective reproduction number [Formula: see text] in the order from high to low is [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], respectively. The global sensitivity analysis shows that the parameters which impact on the effective reproduction number [Formula: see text] are [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in the descending order. Based on the dynamical behavior and the sensitivity analysis of the considered system, the controlling measures are presented to prevent and control the infectious diseases: (1) increasing the nonlinear vaccination rate of the susceptible subpopulation, (2) controlling the number of immigrants to infectious areas, (3) increasing vaccination coverage of immigrants and newborns and (4) improving the effectiveness of vaccines and reducing the rate of immune loss.