Impacts of planktonic components on the dynamics of cholera epidemic: Implications from a mathematical model

Abstract

The aim of this paper is to investigate the role of plankton populations in the aquatic reservoir on the transmission dynamics of acute cholera within the human communities. To this, we develop a nonlinear six dimensional mathematical model that combines the plankton populations with the epidemiological SIR-type human subpopulations and the V. cholerae bacterial population in the aquatic reservoir. It is assumed that the susceptible humans become infected either by ingesting zooplankton, which serves as a reservoir for the cholera pathogen, by free-living V. cholerae in the water, or by cholera-infected individuals. We explore the existence and stability of all biologically plausible equilibria of the system. Also, we determine basic reproduction number (R0) and introduced an additional threshold, named planktonic factor (E0), that is found to significantly affect the cholera transmission. Furthermore, cholera-free equilibrium encounters transcritical bifurcation at R0=1 within the planktonic factor’s unitary range. We perform some sensitivity tests to determine how the epidemic thresholds R0 and E0 will respond to change in the parametric values. The existence of saddle–node bifurcation is shown numerically. Our findings reveal that there are strong connections between the planktonic blooms and the cholera epidemic. We observe that even while eliminating cholera from the human population is very difficult, we may nevertheless lessen the epidemic condition by enhancing immunization, treatment and other preventive measures.