Abstract
Multi-city epidemic models with unrestricted travel, transport-related infection, general nonlinear incidence rate, and seasonality are analyzed. First, a multi-city SIR model is investigated. Seasonality is considered by assuming that the model’s parameters are time-varying and switching. Under this construction, the parameters can be smoothly-varying (for example, due to seasonal changes) or abruptly-varying (for example, due to school holiday breaks). The functional form of the incidence rate is assumed to take a general form that can change in time (for example, due to changes in population behaviour). The effects of transport-related infection and time-varying parameters are studied and some threshold conditions are established which guarantee that the disease-free solution is globally attractive. A screening process and pulse control strategies are applied to the multi-city SIR model in order to investigate and compare the benefits of each strategy. In the pulse control scheme, vaccine failure is considered and the inter-pulse period is not required to equal the seasonal period of the model parameters. Finally, some simulations are given as well as conclusions and future directions.
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