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This study delves into the intricate interplay between social media platforms, interpersonal word-of-mouth communication, and the transmission dynamics associated with non-communicable diseases, with a particular emphasis on type 2 diabetes. Leveraging advanced mathematical modeling and epidemiological methodologies, our objective is to furnish a comprehensive understanding of how information dissemination through digital and interpersonal networks can impact the proliferation of such diseases within populations. We conduct sensitivity analysis to discern the pivotal model parameters that can wield a substantial influence on the dynamics of disease transmission and control. Moreover, we endeavor to explore the capacity of these model parameters to elicit stability or instability within the system. Our focus lies in the rigorous examination of Hopf and transcritical bifurcations within the system. Furthermore, we consider the influence of seasonal fluctuations in the growth rate of social media advertisements with an aim to discern its role in potentially instigating chaotic dynamics within the context of disease progression. In sum, this research seeks to offer a comprehensive and scientifically robust understanding of the patterns of type 2 diabetes and associated communicable diseases within the context of evolving digital communication landscapes.

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.

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 ${{ℛ}}_0$ and show that ${{ℛ}}_0<1$ 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.

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.