Mathematical Analysis of a Cholera Transmission Model Incorporating Media Coverage

Abstract

Diarrhoeal diseases are the major cause of child mortality in developing countries, where access to clean drinking water and sanitation is a problem. In this paper, we develop and analyse a mathematical model for cholera transmission incorporating media coverage. The existence and stability of the equilibrium points is established. Analysis of the model shows that the disease free equilibrium is both locally and globally asymptotically stable when the basic reproduction number is less than unity while the endemic equilibrium is locally asymptotically stable when the reproduction number is greater than unity. Numerical simulations done using the MATLAB software indicate that when media coverage is very efficient, the number of cholera infectives decreases faster, impliying that media alert and awareness campaigns are vital in controlling the spread of cholera.

Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission

“…Since the above deterministic model in equation (2) does not consider stochastic environmental factors and lacks realistic conditions, we extended it to a stochastic model.…”

“…To determine the basic reproduction number (R 0 ) of equations (1) and 2, we use the next generation matrix method by Beryl et al [2]. We have two basic reproduction numbers (deterministic and stochastic).…”

“…Different infectious diseases, like common cold and tuberculosis, are air-borne, whereas some are water-borne like acute water diarrhea (AWD) or cholera (Ochoche [12]). From this, cholera is an infection of small intestine common in developing countries like Asia, Africa, and South and Central America due to poor sanitation and using uncleaned water (Beryl et al [2]). Cholera bacteria shed in their stool for seven to fourteen days, they can infect others through contaminated food or water (Obeng [11]).…”

“…The study done by Fatima et al [7] in Nigeria also proposed a deterministic mathematical model for the control of cholera. Additionally, a lot of authors like Fakai [6], Adewale et al [1], Beryl et al [2], Javidi and Ahmad [8], and others developed mathematical model of cholera to explore the transmission dynamics and controlling strategies. But none of them consider some stochastic environmental factors that can cause cholera outbreaks like, water, rain fall, air temperature, etc.…”

A SIQRB delayed model for cholera and optimal control treatment

“…Furthermore, the authors perform a sensitivity analysis on the key parameters that drive the disease dynamics in order to find their relative importance to cholera's spread and prevalence. In [8], a SIR type model with a class for the bacterial concentration in the environment is proposed, which incorporates media coverage. The existence and stability of the equilibria is analyzed.…”