Bifurcation analysis and optimal control of a network-based SIR model with the impact of medical resources

A new network-based SIR epidemic model, which incorporates the individual medical resource factor and public medical resource factor is proposed. It is verified that the larger the public medical resource factor, the smaller the control reproduction number, and the larger individual medical resource factor can weaken the spread of diseases. We found that the control reproduction number below unity is not enough to ensure global asymptotic stability of the disease-free equilibrium. When the number of hospital beds or the individual medical resource factor is small enough, the system will undergoes backward bifurcation. Moreover, the existence and uniqueness of the optimal control and two time-varying variables’s optimal solutions are obtained. On the scale-free network, the level of optimal control is also proved to be different for different degrees. Finally, the theoretical results are illustrated by numerical simulations. This study suggests that maintaining sufficient both public medical resources and individual medical resources is crucial for the control of infectious diseases.