Modeling the Control of Bacterial Disease by Social Media Advertisements: Effects of Awareness and Sanitation

Abstract

Media impact has significant effect on reducing the disease prevalence, meanwhile sanitation and awareness can control the epidemic by reducing the growth rate of bacteria and direct contacts with infected individuals. In this paper, we investigate the impacts of media and sanitation coverage on the dynamics of epidemic outbreak. We observe that the growth rate of social media advertisements carries out a destabilizing role, while the system regains stability if the baseline number of social media advertisements exceeds a certain threshold. The dissemination of awareness among susceptibles first destabilizes and then stabilizes the system. The disease can be wiped out if the baseline level of awareness or the rate of spreading global information about the disease and its preventive measures is too high. We obtain an explicit expression for the basic reproduction number [Formula: see text] and show that [Formula: see text] leads to the total eradication of infection from the region. To capture a more realistic scenario, we construct the forced delay model by seasonally varying the growth rate of social media advertisements and incorporating the time lag involved in reporting of total infective cases to the policy makers. Seasonal pattern in the growth rate of social media advertisements adds complexity to the system by inducing chaotic oscillations. For gradual increase in the delay in reported cases of infected individuals, the nonautonomous system switches finitely many times between periodic and chaotic states.