Abstract:The problem of stabilizing the spreading process to a prescribed probability distribution over a complex network is considered, where the dynamics of the nodes in the network is given by discrete-time Markov-chain processes. Conditions for the positioning and identification of actuators and sensors are provided, and sufficient conditions for the exponential stability of the desired distribution are derived. Simulations results for a network of N = 10 6 corroborate our theoretical findings.

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Highlights We address the migration of the human population and its effect on pathogen reinfection. We use a Markov-chain SIS metapopulation model over a network. The contact rate is based on the infected hosts and the incidence of their neighboring locations. We estimate from Dengue data in Mexico the dynamics of migration incorporating climate variability.

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