In this paper the problem of designing an output-feedback control for the stabilization of the extinction steady-state in a virus spreading process over a complex network with quarantine is considered. Sufficient conditions are established for the choice of those nodes for which sensor information is necessary and those which should be controlled using notions from constructive control theory. A simple output-feedback control is proposed which exponentially stabilizes the extinction state. Numerical simulation results are provided to illustrate the functioning of the proposed control scheme for a scale-free network of N = 10 6 nodes.

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Most of the recent epidemic outbreaks in the world have a strong immigration component as a trigger rather than the dynamics implied by the basic reproduction number. In this work we present and discuss an approach to the problem of pathogen reinfections in a given area that associates people mobility and transmission of dengue, using a Markov-chain Susceptible-Infected-Susceptible (SIS) metapopulation model over a network. Our model postulates a parameter that we have named the effective inoculum size which represents a local measure of the population size of infected hosts that arrive at a given location as a function of population size, current incidence at neighboring locations and the connectivity of the patches. This parameter can be interpreted as an indicator of outbreak risk of any location. Our model also incorporates climate variability represented by an index based upon precipitation data. We replicate observed patterns of incidence at a regional scale using data from epidemics in Mexico.