Threshold Dynamics of the Switched Multicity Epidemic Models with Pulse Control

This paper mainly studies the threshold dynamics of new multicity HIV (Human Immunodeficiency Virus) epidemic models with switching parameters and pulse control. The model's parameters are assumed to be time-varying functions and switching functional forms in time due to seasonal changes. And the susceptible population is assumed to become infected via shared injections or sexual contacts with infected individuals and pre-AIDS patients (following infection with HIV but before the full development of acquired immune deficiency syndrome). New threshold conditions are established to ensure the extinction of the disease by using Razumikhin-type approach. Pulse control strategies are then applied to the multicity epidemic model and analyzed to guarantee their success in eradicating the disease. Numerical examples are performed to support the analytical results.