The Impact of Transportation Flows on the SEIR Epidemic Model: A Case Study

This study examines how urban transportation systems influence the spatial spread of infectious diseases by developing a modified Susceptible–Exposed–Infected–Recovered (SEIR) model with explicit intercity travel dynamics. The model distinguishes between two mobility mechanisms: travel volume, represented by the departure rate g, and travel speed, represented by the arrival rate $\alpha$. Using the next-generation matrix (NGM) approach, we derive the basic reproduction number $R_0$ and analyse how within-city and transit-phase transmission contribute to epidemic spread. The results show that travel volume and travel speed affect mobility-driven transmission through distinct mechanisms. Increasing g increases the number of travelers entering the transit system and therefore amplifies the aggregate number of transit-mediated infections, although the per-capita transit reproduction expression is governed primarily by $\alpha$ and ${\beta }_d^T$ under the reduced next generation matrix formulation formulation. By contrast, increasing $\alpha$ shortens the time spent in transit, reduces the exposure window during travel, and lowers the per-capita contribution of transit-based infection to $R_0$. Numerical simulations illustrate these effects and support the conclusion that reducing travel volume can mitigate intercity epidemic spread by decreasing the number of potentially exposed travelers. Comparative case studies for Brazil, New Zealand, China, and Algeria are used to evaluate the model under different epidemiological settings and socioeconomic contexts. These socioeconomic indicators are treated as contextual background rather than as direct inputs to the mathematical model. The qualitative predictions of the ordinary differential equation (ODE) model are further cross-validated using an agent-based simulation implemented in NetLogo. Overall, the study shows that separating travel volume from travel speed provides a more precise understanding of mobility-driven disease transmission and can support the design of targeted travel-related control measures.