Influences of Media-Induced Awareness and Sanitation Practices on Cholera Epidemic: A Study of Bifurcation and Optimal Control

Media has a notable impact on reducing disease prevalence, while sanitation measures and heightened awareness can effectively control epidemics by diminishing bacterial growth rates and limiting direct contact with infected individuals. In this study, we propose and analyze an epidemic model to explore how media and sanitation practices influence the dynamics of diseases transmitted through direct contact between susceptible and infected individuals, as well as via bacteria in the environment. Our study entails a combined approach involving both analytical and numerical analyses of the system. We observe that the disease-free and endemic equilibria of the system are interconnected through a forward transcritical bifurcation. We estimate the most important model parameter using authentic cholera data from Sudan for calibration. Our numerical findings suggest that regulating disease transmission through direct contact and environmental bacteria can significantly decrease disease prevalence. Additionally, we note that the growth rate of social media advertisements, along with efforts made by government officials and informed individuals to eliminate bacteria through sanitation coverage, introduces destabilizing effects. However, system stability is reestablished when the baseline number of social media advertisements exceeds a specific threshold. The dissemination of awareness among susceptible individuals, as well as the rate of transfer of informed people to the susceptible class, initially leads to destabilization but eventually stabilizes the system. Disease eradication becomes feasible when the rate of transfer of informed individuals to the susceptible class is very low. Moreover, higher initial values for awareness programs and the dissemination rate of awareness could also eliminate the disease from society. Furthermore, we see that increasing the treatment rate of infectives plays a significant role in achieving disease eradication. Moreover, we investigate an optimal control problem that integrates sanitation interventions and awareness protocols.