Optimal control of an SIVRS epidemic spreading model with virus variation based on complex networks

Xu, Degang; Xu, Xiyang; Xie, Yongfang; Yang, Chunhua

doi:10.1016/j.cnsns.2016.12.025

Cited by 67 publications

(26 citation statements)

References 37 publications

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“…This together with the boundedness of the state variables and coefficients of the controlled system over the finite interval [0, T ], make it possible to use the existence result presented in theorem 9.2.1 in the book of Lukes to prove this theorem. Hence, the following conditions should be satisfied (see the works of Fister et al and Xu et al for similar arguments): (1)The set of solutions of the controlled system and u i ∈ Ω, i = 1,2, is not empty; (2)The control space Ω is closed and convex; (3)The right‐hand side of the controlled system is continuous, bounded, and can be written as a linear function with respect to the controls with coefficients depending on the states; (4)The integrand of the objective functional is convex on Ω with respect to u i , i = 1,2, and there exist constants ρ > 1, C 1 > 0, and C 2 such that

I false(t false) + \frac{1}{2} true \sum_{i = 1}^{2} W_{i} u_{i}^{2} false(t false) ⩾ C_{1} {((), true \sum_{i = 1}^{2} false| u_{i} false(t false) {false|}^{2})}^{ρ false/ 2} - C_{2} .

Attending to the definition of Ω and the nonnegativity of the state variables, the set of solutions of the controlled system with initial conditions and u i ∈ Ω, i = 1,2, is not empty, which proves the Condition 1. The Condition 2 is satisfied since the control set Ω is closed and convex by definition.…”

Section: Optimal Control Problemmentioning

confidence: 99%

Optimal control measures for a susceptible‐carrier‐infectious‐recovered‐susceptible malware propagation model

Gonçalves

Rodrigues

Monteiro

2019

Optim Control Appl Methods

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Purposing to lessen malware propagation, this paper proposes optimal control measures for a susceptible-carrier-infectious-recovered-susceptible (SCIRS) epidemiological model formed by a system of ordinary differential equations. By taking advantage of real-world data related to the number of reported cybercrimes in Japan from 2012 to 2017, an optimal control problem is formulated to minimize the number of infected devices in a cost-effective way. The existence and uniqueness of the results related to the optimality system are proved. Overall, numerical simulations show the usefulness of the proposed control strategies in reducing the spread of malware infections.

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I false(t false) + \frac{1}{2} true \sum_{i = 1}^{2} W_{i} u_{i}^{2} false(t false) ⩾ C_{1} {((), true \sum_{i = 1}^{2} false| u_{i} false(t false) {false|}^{2})}^{ρ false/ 2} - C_{2} .

Section: Optimal Control Problemmentioning

confidence: 99%

Optimal control measures for a susceptible‐carrier‐infectious‐recovered‐susceptible malware propagation model

Gonçalves

Rodrigues

Monteiro

2019

Optim Control Appl Methods

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“…Therefore, the function G(x) is uniformly Lipschitz continuous (satisfying the assumption of condition 1) and satisfies the required bound (5) of the Cesari Theorem. For the proof of condition 3 we refer to reference [34].…”

Section: Existence Of An Optimal Control Pairmentioning

confidence: 99%

Optimal control of a delayed smoking model with immigration

Sun

Jia

2019

Journal of Biological Dynamics

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In this paper, we formulate a smoking model with delay and immigration, and the possibility of optimal controls both over the susceptible and heavy problem smoker subjects is assumed. The existence of the optimal control pair is also proved. We derive the optimality condition via the Pontryagin's maximum principle with delay and obtain the existence of the optimal solution. Numerical simulation is given. Numerical simulations are made to support the main results.

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“…Therefore, the function G ( x ) is uniformly Lipschitz continuous (satisfying the assumption of condition 1) and satisfies the required bound of the Cesari Theorem. For the proof of conditions 3 and 5, we refer to the work of Xu et al Based on the previous discussion, the proof is completed.…”

Section: The Optimal Control Problemmentioning

confidence: 99%

Optimal control of a delayed SIRC epidemic model with saturated incidence rate

Sun

Jia

2018

Optim Control Appl Methods

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In this paper, we present a susceptible-infected-recovered cross-immune (SIRC) epidemic model, which describes Influenza A and analyzes the SIRC epidemic model through the optimal control theory and mathematical analysis. We show the existence of an optimal control pair for the optimal control problem by using Pontryagin's maximum principle with delay and derive the optimality condition.Finally, numerical simulation is carried out to verify our theoretical results. KEYWORDS optimal control, saturated incidence rate, treatment, vaccination(1) Optim Control Appl Meth. 2019;40:367-374.wileyonlinelibrary.com/journal/oca

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Optimal control of an SIVRS epidemic spreading model with virus variation based on complex networks

Cited by 67 publications

References 37 publications

Optimal control measures for a susceptible‐carrier‐infectious‐recovered‐susceptible malware propagation model

Optimal control measures for a susceptible‐carrier‐infectious‐recovered‐susceptible malware propagation model

Optimal control of a delayed smoking model with immigration

Optimal control of a delayed SIRC epidemic model with saturated incidence rate

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