A Between-Host Cholera Mathematical Model Incorporating Temperature Dependence

Abstract

This paper establishes a between-host cholera model with temperature dependent parameter. This is done using system of ODEs to analyse the effect of temperature change on cholera disease. The model analysis reveals that when R0 < 1, the disease free equilibrium point is locally and globally asymptotically. It is also noticed that if R0 > 1, the endemic equilibrium point is locally and globally asymptotically stable. The sensitivity analysis of model parameters shows that R0 ​depends intensively on infection rate of pathogen α1​ normalized with temperature. An increase in infection rate of pathogen α1​ that is dependent on temperature by 10% would increase R0​ by 10% and decreasing it by 10% reduces R0 by 10%; hence, increasing the temperature of the environment where the pathogen lives would help reduce the rate of infection of the pathogen, thus reducing the reproduction number R0​. We conducted numerical simulation of the model in response to temperature changes, and the results indicate that Vibrio cholerae pathogens multiply faster at 23°C but between 23°C < T ≤ 43°C the pathogen multiplication is hindered, therefore, at 23°C, more pathogens are active to cause infection compared to high temperatures.