Dynamics of disease spread in evolving susceptible networks

Disease outbreaks often begin within a small group of the population and spread through contact. While all population may be biologically susceptible, only those interacting with infectious individuals form the true target population and responsible for the disease transmission. To capture this reality, we develop a compartmental model incorporating dynamic contacts and an evolving target susceptible population. Applied to COVID-19 data in Nepal, the model accurately produces the timing, magnitude, and shape of three major epidemic waves, aligns closely with reported seroprevalence (8-11% post-first wave, 63-69% post-second wave), and reveals significant under-reporting of cases. Sensitivity analyses highlight the critical role of the target population expansion rate in driving epidemic severity, with higher values escalating peak infections and cumulative cases. The basic reproduction number (R₀) is primarily influenced by the size of the target population, underscoring the need to limit high-risk exposure. Sensitivity and threshold analyses further identify the target population expansion rate as a critical parameter, beyond which the epidemic rapidly increases in magnitude. Our findings demonstrate that strategic interventions reducing transmission rates, controlling target population expansion, and managing contact network transitions can significantly mitigate epidemic burden and enhance the likelihood of disease extinction. In addition to numerical simulations, we rigorously study the analytical properties of the proposed model and identify an extinction threshold index that governs whether the disease dies out or persists. This evolving network model offers a robust framework for real-time epidemic assessment, adaptive policy making, and improved pandemic preparedness.