SIS Epidemic Model under Mobility on Multi-layer Networks

Abhishek, Vishal; Srivastava, Vaibhav

doi:10.23919/acc45564.2020.9147631

Cited by 7 publications

(2 citation statements)

References 24 publications

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“…12 q 1 12 0 0 −q 1 23 q 1 23 0 q 1 32 −q 1 32 , and Q 2 = −q 2 12 q 2 12 0 q 2 21 −q 2 21 0 0 q 2 32 −q 2 32 .…”

Section: Discussionmentioning

confidence: 99%

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SIS Epidemic Spreading under Multi-layer Population Dispersal in Patchy Environments

Abhishek¹,

Srivastava²

2022

Preprint

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We study SIS epidemic spreading models under population dispersal on multi-layer networks. We consider a patchy environment in which each patch comprises individuals belonging to different classes. Individuals disperse to other patches on a multi-layer network in which each layer corresponds to a class. The dispersal on each layer is modeled by a Continuous Time Markov Chain (CTMC). At each time, individuals disperse according to their CTMC and subsequently interact with the local individuals in the patch according to an SIS model. We establish the existence of various equilibria under different parameter regimes and establish their (almost) global asymptotic stability using Lyapunov techniques. We also derive simple conditions that highlight the influence of the multi-layer network on the stability of these equilibria. For this model, we study optimal intervention strategies using a convex optimization framework. Finally, we numerically illustrate the influence of the multilayer network structure and the effectiveness of the optimal intervention strategies.

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“…12 q 1 12 0 0 −q 1 23 q 1 23 0 q 1 32 −q 1 32 , and Q 2 = −q 2 12 q 2 12 0 q 2 21 −q 2 21 0 0 q 2 32 −q 2 32 .…”

Section: Discussionmentioning

confidence: 99%

“…where w is a positive left eigenvector of (BM + L * ) such that w (BM + L * ) = 0 with max i w i = 1, M = I − F * , s = min i,α (δ α i − β α i ), W = diag(w), and λ 2 is the second smallest eigenvalue of 1 2 W (BM + L * ) + (BM + L * ) W .…”

Section: Analysis Of Sis Model With Multi-layer Population Dispersalmentioning

confidence: 99%