Vol. 4, Issue 1, Part A (2022)

among which media coverage and emigration patterns hold significant relevance. This paper develops and analyzes a mathematical model that integrates the dual impacts of media-modified transmission rates and emigration-dependent population changes on disease progression. The role of media is represented through a reduction in transmission rates, driven by heightened public awareness and behavioral adjustments stemming from media campaigns. Concurrently, emigration is modelled as a dynamic factor influenced by infection prevalence, which alters population structures and modifies disease spread both in source and destination regions.

The analysis reveals that increased media intensity significantly curtails the reproduction number and hastens the attainment of a disease-free state. However, emigration presents a dual challenge-it can reduce infection levels in the source population while simultaneously elevating risks in receiving populations. Through stability analysis and numerical simulations, the interplay between media effectiveness and emigration rates is quantified, providing critical insights into their roles in epidemic mitigation. This study underscores the importance of incorporating these factors into public health strategies and disease management policies, offering actionable recommendations for optimizing media campaigns and monitoring emigration flows to achieve effective disease control. The findings hold practical relevance for policymakers, epidemiologists, and global health practitioners, highlighting the need for an integrated approach to managing infectious disease outbreaks in interconnected societies.