Exploring noise-induced dynamics and optimal control strategy of iSIR cholera transmission model

Few existing studies establish the fact that although human pathogen exists in the environmental reservoir, infectious disease outbreak is rare. In this article, we investigate the dynamics of cholera disease where the transmission occurs via contact with a contaminated reservoir. A deterministic iSIR compartmental epidemic model is formulated and explored the realistic situation, in which the quantity of ingested pathogens must exceed a critical threshold, the minimal infectious dose (MID), in order to infect healthy population. Bacteria growth rate is considered to follow the Allee effect. This model system shows multi-stability and undergoes transcritical and saddle-node bifurcations with respect to various parameters. Thus, external environmental noise can give rise to observable dynamics for the stochastic counterpart. One can see a noise-induced frequent transitions between two separate interior attractors, in particular for the cases where the deterministic model displays bistability. The global sensitivity using PRCC method is performed. Also, the optimal control for the developed deterministic cholera epidemic model is carried out with numerical illustrations. Our model primarily designed to explain and predict the indirectly transmitted cholera epidemic model incorporating the idea of MID. This study gives a different outlook for the transmission of disease from the human-centered perspective to socioeconomic context.