Modelling the impact of media coverage on cholera transmission

Paper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.Cholera is a highly infectious disease caused by the bacterium Vibrio cholerae. Its spread is a product of both social and environmental factors. Past and recent cholera outbreaks in Kenya haveled to deaths and hospitalisation. In this study, we investigate the impact of media coverage on the spread of cholera using a mathematical model whose formulation is based on a system of ordinary differential equations. Positivity and boundedness of solutions are established to ensure that the model is well posed. The basic reproduction number is derived using the next generation matrix approach and used in analysing the local stability of the disease free equilibrium. sensitivity analysis of the basic reproduction number with respect to the model parameters is carried out to access the relative impact of each parameter on the spread of the disease. The results show that increasing the efficacy of media coverage is vital in controlling the spread of cholera

An immuno-epidemiological model linking between-host and within-host dynamics of cholera

Cholera, a severe gastrointestinal infection caused by the bacterium Vibrio cholerae, remains a major threat to public health, with a yearly estimated global burden of 2.9 million cases. Although most existing models for the disease focus on its population dynamics, the disease evolves from within-host processes to the population, making it imperative to link the multiple scales of the disease to gain better perspectives on its spread and control. In this study, we propose an immuno-epidemiological model that links the between-host and within-host dynamics of cholera. The immunological (within-host) model depicts the interaction of the cholera pathogen with the adaptive immune response. We distinguish pathogen dynamics from immune response dynamics by assigning different time scales. Through a time-scale analysis, we characterise a single infected person by their immune response. Contrary to other within-host models, this modelling approach allows for recovery through pathogen clearance after a finite time. Then, we scale up the dynamics of the infected person to construct an epidemic model, where the infected population is structured by individual immunological dynamics. We derive the basic reproduction number ($\mathcal{R}_0$) and analyse the stability of the equilibrium points. At the disease-free equilibrium, the disease will either be eradicated if \mathcal{R}_0 < 1 or otherwise persists. A unique endemic equilibrium exists when \mathcal{R}_0 > 1 and is locally asymptotically stable without a loss of immunity