The impact of migration-mediated multi-threshold control strategies on disease spread of a Filippov patch epidemic...

In this paper, a two-patch epidemic model incorporating migration-mediated multi-threshold control strategies is proposed to explore the effect of migration and adaptive interventions (e.g, lockdown) on disease transmission. If the numbers of infected individuals in both patches are below a predefined threshold (I₁ < I_c, I₂ < I_c), migration between patches could occur freely; if I_i>I_c(i=1or2), the ith patch would be put under surveillance with a partial lockdown, only essential personnels (e.g., healthcare workers) could migrate between patches at saturated rates; if I₁ > I_c, I₂ > I_c, a complete lockdown would be imposed on both patches. The global dynamics of proposed Filippov system is analysed, including the existence and stability of disease-free, boundary, and endemic equilibria. Especially, the sliding mode dynamics on switching surfaces, i.e., multiple pseudo-equilibria and bifurcations (e.g., saddle-node, Hopf, Bogdanov-Takens and period-halving) are discussed in detail, which could exactly characterize the critical tipping points in epidemic transmission trajectories. Numerical simulations demonstrate that if some appropriate thresholds on migration regulation between two patches are chosen, the number of infected individuals can be effectively controlled at a desired low level, which could further potentially curb the disease spread.