Global analysis of a periodic epidemic model on cholera in presence of bacteriophage

Abstract

We propose and analyze a recurrent epidemic model of cholera in the presence of bacteriophage. The model is extended by general periodic incidence functions for low-infectious bacterium and high-infectious bacterium, respectively. A general periodic shedding function for two infected class (phage-positive and phage-negative) and a generalized contact and intrinsic growth function for susceptible class are also considered. Under certain biological assumptions, we derive the basic reproduction number (R0) in a periodic environment for the proposed model. We also observe the global stability of the disease-free equilibrium, existence, permanence, and global stability of the positive endemic periodic solution of our proposed model. Finally, we verify our results with specific functional form.