Diffusion-driven disease dynamics under induced psychological fear and healthcare interventions

A widespread epidemic poses multiple risks to society at large, causing systemic economic destabilization and undermining global health issues. Awareness initiatives include reshaping public perception and influencing individual behavioral response. By utilizing media as a dynamic variable, healthcare professionals and policy makers can effectively promote non-pharmaceutical proactive measures. Migration creates complex disease transmission pathways where public movement becomes a critical vector for a potential epidemic propagation. Therefore, our research proposes and analyzes a diffusion-driven nonlinear epidemic model to investigate the effect of psychological fear and limited healthcare facilities on the direct transmission patterns of infectious diseases. This research investigates the existence and uniqueness of the non-negative equilibrium, its boundedness and nonlinear stability characteristics. The next-generation matrix technique is utilized to calculate the basic reproduction number ([Formula: see text]). Our model is calibrated by incorporating actual COVID-19 data from four countries (Norway, Italy, India and Greece) and establishing important epidemiological parameters through estimation. We further analyzed the basic reproduction number [Formula: see text] across four different countries to assess which parameters responded more effectively to the global pandemic. Global sensitivity analysis, utilizing the partial rank correlation coefficient (PRCC), is conducted to evaluate the most influential parameters that have significant impact on epidemic threshold and infected individuals. A slight variation in the control parameter induces transcritical and Hopf-bifurcations, both forward and backward. Center manifold theory is used to analyze the transcritical case, revealing a backward bifurcation, implying disease persistence even when [Formula: see text]. The study reveals that heightened psychological fear within the population may diminish the magnitude of periodic oscillations, and if a specific threshold of fear is surpassed, these oscillations halt, resulting in the stabilization of endemic equilibrium at a reduced level. The numerical investigation indicates that the disease burden can be mitigated by increased adaptability of medical resources through hospitalization and non-pharmaceutical interventions as a result of media influence. Further, our diffusion model analysis findings also indicate that public movement may boost disease transmission and lead to emergence of a distinctive structural phenomenon termed as an endemic bubble in the region under investigation.