Metadata about: Measles and influenza are two major diseases–caused an epidemic in India. Therefore, in this paper, a [Formula: see text] 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 [Formula: see text] , which is determined by the next-generation approach and obtained that if [Formula: see text] , the disease-free equilibrium exists and it is locally as well as globally asymptotically stable. Further for [Formula: see text] , 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.

About: Measles and influenza are two major diseases–caused an epidemic in India. Therefore, in this paper, a [Formula: see text] 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 [Formula: see text] , which is determined by the next-generation approach and obtained that if [Formula: see text] , the disease-free equilibrium exists and it is locally as well as globally asymptotically stable. Further for [Formula: see text] , 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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