Abstract
Measles and influenza are two major diseases–caused an epidemic in India. Therefore, in this paper, a { SVEIRS} epidemic mathematical model for measles and influenza is proposed and analyzed, where pre and post vaccinations are considered as control strategies with waning natural, vaccine-induced immunity and saturation incidence rate. The dissection of the proposed model is conferred in terms of the associated reproduction number {mathcal {R}}_v, which is determined by the next-generation approach and obtained that if {mathcal {R}}_vle 1, the disease-free equilibrium exists and it is locally as well as globally asymptotically stable. Further for {mathcal {R}}_v> 1, a unique endemic equilibrium exists and it is also locally as well as globally asymptotically stable under certain conditions, which shows the prevalence and persistence of the disease in the population.
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