INVESTIGATION OF THE IMPACT OF ONE-WAY MOBILITY IN A MATHEMATICAL MODEL OF COVID-19 TRANSMISSION: STABILITY ANALYSIS AND NUMERICAL SIMULATIONS - Muhammad Afief Balya; Yuni Yulida; Sila Rizqina; Hermei Lissa (Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat, 2026)
This study develops a COVID-19 transmission model incorporating one-way human mobility between two interconnected cities to examine the epidemiological consequences of asymmetric population movement. Unlike most existing models that assume symmetric two-way mobility, and extending the no-mobility framework of (Balya et al., 2025), the proposed model introduces unidirectional population flow by allowing individuals from only one city to engage in high-mobility activities, thereby generating directed movement that reflects realistic patterns such as commuting, migration, and unequal social interaction. The basic reproduction number is analytically derived using the Next Generation Matrix approach, and the stability of the disease-free equilibrium is established through the Van den Driessche–Watmough method. Elasticity analysis demonstrates that mobility-related parameters substantially increase , while recovery and mortality parameters reduce it, highlighting key factors that drive transmission under directed movement. Numerical simulations across three epidemiological scenarios, defined by the relative ordering of the two cities’ no-mobility reproduction numbers, show that one-way mobility raises the basic reproduction number of the coupled system to approximately 3.99, 2.10, and 1.62, respectively, and consistently elevates infection levels in both cities, even when one city is subcritical in isolation, due to both imported infections and intensified local contact rates. These results suggest that mobility-sensitive interventions, such as movement restrictions on high-mobility populations or social distancing measures in high-transmission cities are essential to prevent directed population flow from destabilizing epidemic control across interconnected regions.