Why to consider environmental pollution in cholera modeling?

Abstract

Communicated by: M. Efendiev MOS Classification: 92B05 92D30 34D20We propose a deterministic model to study the impact of environmental pollution on the dynamics of cholera. We consider both human to human and human-environment-human transmission modes in our model. We obtain the expression for the basic reproduction number of the proposed model. The study of our model reveals that environmental pollution plays a significant role in the spread of cholera and should not be ignored. Although various dimensions of cholera has been studied using mathematical models but scanty efforts have been made to understand impact of environmental pollution on this disease. Through this study, we try to bridge this gap.

Backward bifurcation in a cholera model with a general treatment function

“…Despite its popularity in infectious disease models, the backward bifurcation is generally absent in waterborne pathogen models [21,26,27,29,30,37,40]. However, recently some mathematical models pertaining to waterborne diseases with limited treatment facilities exhibit backward bifurcation [28,39].…”

Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru

“…Since all the compartments in the proposed model consist of the human population, they have to be non-negative for any arbitrary time 't'. We have used the technique used in [30,33], to prove the positivity of solutions. The following theorem establishes the positivity of the solution.…”