Nonlinear dynamical analysis and control strategies of a network-based SIS epidemic model with time delay. (English) Zbl 1464.92255
Summary: In this paper, we establish a susceptible-infected-susceptible (SIS) epidemic model with nonlinear incidence rate and time delay on complex networks. Firstly, according to the existence of a positive equilibrium point, we work out the threshold values \(R_0\) and \(\lambda_c\) of disease propagation. Secondly, we demonstrate the stabilities of the disease-free equilibrium point and the disease-spreading equilibrium point by constructing Lyapunov function and applying delay differential equations theorem. Thirdly, four different control strategies are investigated and compared, including uniform immunization control, acquaintance immunization control, active immunization control and optimal control. Finally, we perform representative numerical simulations to illustrate the theoretical results and further discover that the nonlinear incidence rate can more accurately reflect individual psychological activities when a certain disease outbreaks at a high level.
MSC:
| 92D30 | Epidemiology |
| 34D23 | Global stability of solutions to ordinary differential equations |
| 34H05 | Control problems involving ordinary differential equations |
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