Dynamics of a network-based SIR epidemic model with double impulsive controls.

A network-based susceptible-infected-recovered (SIR) epidemic model is proposed to study the spread of infectious diseases, thereby incorporating vertical transmission and a saturated incidence rate. Additionally, it introduces double impulsive control strategies, including pulse vaccination and screening with treatment at distinct fixed intervals. Dynamical behaviors of the formulated model are analyzed using two types of transmission thresholds, namely $ R^0_{k_i} $ and $ \widehat{R^0_{k_i}} $. By applying the Floquet theorem and comparison principle, the system admits a disease-free periodic solution that is globally asymptotically stable if $ \max\limits_{i = 1, 2, \ldots, n}\widehat{R^0_{k_i}} < 1 $. The persistence of disease is confirmed from the uniform persistence of the Poincaré map when $ \frac{1}{1+\alpha}\max\limits_{i = 1, 2, \ldots, n}R^0_{k_i} > 1 $, where $ \alpha $ is the saturated coefficient in the saturation infection. Scenario studies are performed to numerically evaluate the impact of various parameters on the disease dynamics, and the effectiveness of double impulsive controls. It can be concluded that synthetical double impulsive controls are more efficient at eradicating the disease compared with only either of them.