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.