Modeling the effects of psychological fear, media-induced awareness, and sanitation efforts on the dynamics of bacterial diseases

Abstract

Bacterial diseases significantly impact human health and the economy, posing serious challenges to societal well-being. Psychological fear of infection motivates behavioral changes to reduce contacts with infected individuals. Awareness campaigns play a crucial role in educating the public about precautionary measures, thereby reducing the likelihood of bacteria ingestion from contaminated sources. Furthermore, individuals who are informed through such campaigns often implement sanitation practices that help to reduce bacterial density in the environment. This study develops a nonlinear mathematical model to analyze the effects of psychological fear, media-induced awareness, and sanitation practices on bacterial disease dynamics. The model considers infection transmission through direct contacts with infected individuals and indirect exposure to environmental bacteria, assuming bacterial density increases proportional to the infected population. Results show that psychological fear, media-driven awareness, and sanitation play crucial roles in shaping bacterial disease dynamics. A higher growth rate of media advertisements induces limit cycle oscillations in the system via Hopf-bifurcation. However, these oscillations diminish when psychological fear surpasses a threshold. Furthermore, it is found that increasing efficacy of media advertisements in promoting precautionary behaviors and enhancing the depletion rate of bacteria through sanitation efforts by aware individuals can reduce disease prevalence. However, these measures may also induce periodic oscillations by lowering the Hopf-bifurcation threshold for media advertisements growth. An increase in the depletion rate of bacteria due to sanitation efforts can also lead to stability switch via double Hopf-bifurcation, underscoring the need for balanced sanitation strategies to prevent oscillations while ensuring effective disease control.