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