Chaos in a nonautonomous model for the impact of media on disease outbreak

Abstract

Social media initiatives educate the public about the tools and strategies necessary to defend themselves from emerging diseases. The effect of media advertisements in combating an infectious disease is explored in the present investigation. The numerical results show that the system destabilizes when the growth rate of media advertisements goes above a certain value. For lower ranges of the rate of distribution of awareness through social media platforms, our system showcases stable endemic state. But as the rate of disseminating awareness surpasses a critical value, the system undergoes a Hopf bifurcation and limit cycle oscillations appear. However, the persistent oscillations are killed out and the system returns to a stable endemic state as the rate of distribution of awareness exceeds another threshold value. Extremely large values of the awareness distribution through media advertisements eradicate the disease from the entire community. Model parameters with significant impacts on the disease prevalence and eradication are identified through sensitivity analysis. We extend our model to encapsulate the seasonal variation in the rate of media advertisements. Sufficient conditions have been derived for which the nonautonomous system exhibits globally attractive positive periodic solution. The nonautonomous system is shown to produce chaotic dynamics under the circumstances of the corresponding autonomous system that exhibits limit cycle oscillations. Overall, our findings deduce that media advertisements play a critical role in raising public awareness and ultimately resulting in the eradication of the disease from the society.