The optimal dynamic immunization under a controlled heterogeneous node-based SIRS model

Lu-Xing Yang, Moez Draief and Xiaofan Yang

Physica A: Statistical Mechanics and its Applications, 2016, vol. 450, issue C, 403-415

Abstract: Dynamic immunizations, under which the state of the propagation network of electronic viruses can be changed by adjusting the control measures, are regarded as an alternative to static immunizations. This paper addresses the optimal dynamical immunization under the widely accepted SIRS assumption. First, based on a controlled heterogeneous node-based SIRS model, an optimal control problem capturing the optimal dynamical immunization is formulated. Second, the existence of an optimal dynamical immunization scheme is shown, and the corresponding optimality system is derived. Next, some numerical examples are given to show that an optimal immunization strategy can be worked out by numerically solving the optimality system, from which it is found that the network topology has a complex impact on the optimal immunization strategy. Finally, the difference between a payoff and the minimum payoff is estimated in terms of the deviation of the corresponding immunization strategy from the optimal immunization strategy. The proposed optimal immunization scheme is justified, because it can achieve a low level of infections at a low cost.

Keywords: Electronic virus; Controlled heterogeneous node-based model; Optimal dynamic immunization; Optimal control scheme; Pontryagin Minimum Principle; Network topology (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:450:y:2016:i:c:p:403-415

DOI: 10.1016/j.physa.2016.01.026

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