Optimal Control Strategies for Virus Spreading in Inhomogeneous Epidemic Dynamics

2013 ◽  
Vol 56 (3) ◽  
pp. 621-629 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Optimal Control ◽  
Cyber Security ◽  
Transmission Rate ◽  
Control Strategies ◽  
High Reliability ◽  
Threshold Function ◽  
Epidemic Dynamics ◽  
Sis Epidemic Model ◽  
The Cost ◽  
Virus Spreading

Abstract.In this paper, we study the spread of virus/worm in computer networks with a view to addressing cyber security problems. Epidemic models have been applied extensively to model the propagation of computer viruses, which characterize the fact that infected machines may spread malware to other hosts connected to the network. In our framework, the dynamics of hosts evolves according to a modified inhomogeneous Susceptible-Infectious-Susceptible (SIS) epidemic model with time-varying transmission rate and recovery rate. The infection of computers is subject to direct attack as well as propagation among hosts. Based on optimal control theory, optimal attack strategies are provided by minimizing the cost (equivalently maximizing the profit) of the attacker. We present a threshold function of the fraction of infectious hosts, which captures the dynamically evolving strategies of the attacker and reflects the persistence of virus spreading. Moreover, our results indicate that if the infectivity of a computer worm is low and the computers are installed with antivirus software with high reliability, the intensity of attacks incurred will likely be low. This agrees with our intuition.

scholarly journals Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 929
Author(s):  
Guiyun Liu ◽  
Jieyong Chen ◽  
Zhongwei Liang ◽  
Zhimin Peng ◽  
Junqiang Li
Keyword(s):  
Optimal Control ◽  
Rapid Development ◽  
Hamiltonian Function ◽  
Propagation Model ◽  
Dynamical Analysis ◽  
Optimal Control Strategy ◽  
Epidemic Dynamics ◽  
Optimization Control ◽  
The Cost ◽  
The Pontryagin Maximum Principle

With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R0, the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.

scholarly journals The Dynamics and Optimal Control of a Hand-Foot-Mouth Disease Model

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Hongwu Tan ◽  
Hui Cao
Keyword(s):  
Optimal Control ◽  
Reproduction Number ◽  
Control Strategies ◽  
Disease Model ◽  
Mouth Disease ◽  
Infected People ◽  
Hand Foot Mouth Disease ◽  
The Cost ◽  
Existence Of Equilibria ◽  
Disease Free

We build and study the transmission dynamics of a hand-foot-mouth disease model with vaccination. The reproduction number is given, the existence of equilibria is obtained, and the global stability of disease-free equilibrium is proved by constructing the Lyapunov function. We also apply optimal control theory to the hand-foot-mouth disease model. The treatment and vaccination interventions are considered in the hand-foot-mouth disease model, and the optimal control strategies based on minimizing the cost of intervention and minimizing the number of the infected people are given. Numerical results show the usefulness of the optimization strategies.

scholarly journals Multiple Control Strategies for Prevention of Avian Influenza Pandemic

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Roman Ullah ◽  
Gul Zaman ◽  
Saeed Islam
Keyword(s):  
Optimal Control ◽  
Avian Influenza ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Antiviral Treatment ◽  
Cost Effective ◽  
Effective Control ◽  
Multiple Control ◽  
Control Functions ◽  
The Cost

We present the prevention of avian influenza pandemic by adjusting multiple control functions in the human-to-human transmittable avian influenza model. First we show the existence of the optimal control problem; then by using both analytical and numerical techniques, we investigate the cost-effective control effects for the prevention of transmission of disease. To do this, we use three control functions, the effort to reduce the number of contacts with human infected with mutant avian influenza, the antiviral treatment of infected individuals, and the effort to reduce the number of infected birds. We completely characterized the optimal control and compute numerical solution of the optimality system by using an iterative method.

scholarly journals Modelling the Periodic Outbreak of Measles in Mainland China

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yuyi Xue ◽  
Xiaoe Ruan ◽  
Yanni Xiao
Keyword(s):  
Optimal Control ◽  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Control Strategies ◽  
Mainland China ◽  
Asymptomatic Infection ◽  
Protection Measures ◽  
The Basic Reproduction Number

In mainland China, measles infection reached the lowest level in 2012 but resurged again after that with a seasonally fluctuating pattern. To investigate the phenomenon of periodic outbreak and identify the crucial parameters that play in the transmission dynamics of measles, we formulate a mathematical model incorporating periodic transmission rate and asymptomatic infection with waning immunity. We define the basic reproduction number as the threshold value to govern whether measles infection dies out or not. Fitting the reported measles cases from 2013 to 2016 to our proposed model, we estimate the basic reproduction number R0 with immunization to be 1.0077. From numerical simulations, we conclude asymptomatic infection does not cause much new infections and the key parameters affecting the transmission of measles are vaccination rate, transmission rate, and recovery rate, which suggests the public to enhance vaccination and protection measures to reduce effective contacts between susceptible and infective individuals and treat infected individuals timely. To minimize the number of infected individuals at a minimal cost, we formulate an optimal control system to design optimal control strategies. Numerical simulations show the effectiveness of optimal control strategies and recommend us to implement the control strategies as soon as possible. In particular, enhancing vaccination is especially effective in lowering the initial outbreak and making disease recurrence less likely.

Performance Characterization of the Novel Topology for High-Frequency Isolation Bi-Directional DC/DC Converter

2013 ◽  
Vol 273 ◽  
pp. 305-309 ◽  
Author(s):  
Peng Hui Jing ◽  
Cong Wang ◽  
Jun Wang ◽  
Feng Zhao
Keyword(s):  
High Frequency ◽  
Power Flow ◽  
Control Strategies ◽  
High Reliability ◽  
Input Voltage ◽  
Phase Shifting ◽  
Matlab Simulation ◽  
High Input ◽  
The Cost ◽  
Bidirectional Power Flow

A novel topology of high-frequency isolation bi-directional DC/DC converter used in high-Input low-output system was proposed, which has not only the advantages, such as enabling bidirectional power flow, ease of realizing soft-switching control, galvanic isolation, high reliability and so on, but also can be used in high-input voltage application and apparently decreases the stress of the switches, which reduces the cost of the converter, improves power density and the efficiency of the converter. According to the different work condition, two control strategies are analyzed in this paper: the traditional phase shifting control (TPC) and PWM plus phase shifting control (PPC), which further improves the overall efficiency of the converter. The MATLAB simulation has been done to verify the feasibility of the proposed DC/DC converter and accuracy of the criterion.

scholarly journals Measles dynamics on network models with optimal control strategies

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yuyi Xue ◽  
Xiaoe Ruan ◽  
Yanni Xiao
Keyword(s):  
Optimal Control ◽  
Transmission Rate ◽  
Control Strategies ◽  
Random Network ◽  
Network Models ◽  
Control Measures ◽  
Effective Control ◽  
Threshold Dynamics ◽  
Heterogeneous Model ◽  
Strong Control

AbstractTo investigate the influences of heterogeneity and waning immunity on measles transmission, we formulate a network model with periodic transmission rate, and theoretically examine the threshold dynamics. We numerically find that the waning of immunity can lead to an increase in the basic reproduction number $R_{0}$ R 0 and the density of infected individuals. Moreover, there exists a critical level for average degree above which $R_{0}$ R 0 increases quicker in the scale-free network than in the random network. To design the effective control strategies for the subpopulations with different activities, we examine the optimal control problem of the heterogeneous model. Numerical studies suggest us no matter what the network is, we should implement control measures as soon as possible once the outbreak takes off, and particularly, the subpopulation with high connectivity should require high intensity of interventions. However, with delayed initiation of controls, relatively strong control measures should be given to groups with medium degrees. Furthermore, the allocation of costs (or resources) should coincide with their contact patterns.

scholarly journals Analysis of Optimal Control Strategies for Preventing Computer Virus Infection and Reduce Program Files Damage with Other Symptoms

2021 ◽  
pp. 8-29
Author(s):  
Titus Ifeanyi Chinebu ◽  
Ikechukwu Valentine Udegbe ◽  
Edmund Onwubiko Ezennorom
Keyword(s):  
Optimal Control ◽  
Positive Impact ◽  
Control Strategies ◽  
Computer Virus ◽  
Computer Performance ◽  
Control Functions ◽  
Infection Dynamics ◽  
Treatment Function ◽  
Saturated Incidence ◽  
The Cost

Program files damage and other computer virus symptoms has become a very threatening issue to computer performance. This paper considered an  model with incidence of infected and program files damaged computers and saturated incidence of vaccination and treatment function. Two control functions have been used; one for vaccinating the susceptible computer population and the other for the treatment of the program files damaged computer population. The Pontryagin’s Maximum Principle has been used to characterize the optimal control whose numerical results show the positive impact of the two controls used for controlling the infection dynamics of computer virus. Actually the intention of this study is to minimize the number of infected and program files damaged computer systems and at the same time minimize the cost associated to the controls. Efficiency analysis is also studied to determine the best control strategy among vaccination and treatment. Numerical simulations were carried out in this model to demonstrate the analytical results and it was revealed that combination of vaccination and treatment is the most successful way to minimize the incidence of program files damage. 

scholarly journals Bifurcation and Stabillity Analysis of HIV Transmission Model with Optimal Control

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Kumama Regassa Cheneke ◽  
Koya Purnachandra Rao ◽  
Geremew Kenassa Edessa
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Hiv Transmission ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Control Measures ◽  
Transmission Model ◽  
Progression Rate ◽  
Asymptotically Stable ◽  
The Cost

A mathematical model of HIV transmission is built and studied in this paper. The system’s equilibrium is calculated. A next-generation matrix is used to calculate the reproduction number. The novel method is used to examine the developed model’s bifurcation and equilibrium stability. The stability analysis result shows that the disease-free equilibrium is locally asymptotically stable if 0 < R 0   < 1 but unstable if R 0 > 1 . However, the endemic equilibrium is locally and globally asymptotically stable if R 0 > 1 and unstable otherwise. The sensitivity analysis shows that the most sensitive parameter that contributes to increasing of the reproduction number is the transmission rate β 2 of HIV transmission from HIV individuals to susceptible individuals and the parameter that contributes to the decreasing of the reproduction number is identified as progression rate η of HIV-infected individuals to AIDS individuals. Furthermore, it is observed that as we change η from 0.1 to 1 , the reproduction number value decreases from 1.205 to 1.189, where the constant value of β 2 = 0.1 . On the other hand, as we change the value of β 2 from 0.1 to 1 , the value of the reproduction number increases from 0.205 to 1.347, where the constant value of η = 0.1 . Further, the developed model is extended to the optimal control model of HIV/AIDS transmission, and the cost-effectiveness of the control strategy is analyzed. Pontraygin’s Maximum Principle (PMP) is applied in the construction of the Hamiltonian function. Moreover, the optimal system is solved using forward and backward Runge–Kutta fourth-order methods. The numerical simulation depicts the number of newly infected HIV individuals and the number of individuals at the AIDS stage reduced as a result of taking control measures. The cost-effectiveness study demonstrates that when combined and used, the preventative and treatment control measures are effective. MATLAB is used to run numerical simulations.

scholarly journals A Quantitative Analysis of Preventive Measures to Mitigate the Infectious Diseases Using SIR model by Optimal Control Technique

2018 ◽  
Vol 5 (1) ◽  
pp. 11-19
Author(s):  
Jakia Sultana ◽  
Samiha Islam Tanni ◽  
Shamima Islam
Keyword(s):  
Optimal Control ◽  
Infectious Diseases ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Transmission Rate ◽  
Control Strategies ◽  
Sir Model ◽  
The State ◽  
Control Technique ◽  
State Equations

Optimal Control Problem with the state equations which describes the standard SIR Model is studied here. We considered the SIR Model with vaccination and without vaccination. We formulated an optimal control problem and derived necessary conditions. Existence of the state and the objective functional are also verified. We also characterized the optimal control by Pontryagin’s maximum principle which minimizes the number of infected individuals and cost of vaccination over some finite period. Whenever the vaccination is carried out for a long period of time, the simulated result effectively works for disease with high transmission rate. Observations from the numerical simulation revels that the infectious diseases are most successfully controlled whenever control strategies were adopted at early stages. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 11-19

scholarly journals Optimal Control Analysis of an Age-Structured Malaria Model Incorporating Children under Five Years and Pregnant Women

2019 ◽  
pp. 1-23
Author(s):  
George Theodore Azu-Tungmah ◽  
Francis T. Oduro ◽  
Gabriel A. Okyere
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Pregnant Women ◽  
Control Strategies ◽  
Cost Effectiveness Analysis ◽  
Under Five ◽  
Effectiveness Analysis ◽  
Age Structured ◽  
The Cost ◽  
Malaria Model

In this article, we apply the optimal control theory to a new age-structured malaria model with three infectious compartments for people under five years, over five years and pregnant women. The model is formulated for malaria endemic areas in the world and the following malaria control strategies ITN, IRS, Chemoprophylaxis and Improved Clinical Treatment were examined and analysed on the mode. The Cost-effectiveness Analysis points out that more attention should be given Insecticide -Treated bed nets (ITNs) in order to eliminate the malaria disease globally because the female Anopheles mosquitoes need human blood to lay their eggs. The expression for the effective reproduction number  has been derived by using the next-generation method. The impact of the controls on the was studied and it came out that all the four controls have a positive impact such that the ITNs can reduce to zero as the value of ITNs approaches one. Pontryagin’s Maximum Principle was applied to analyse the optimal control model theoretically and the optimality system was solved numerically through an iterative scheme. The optimal plots (Figs. 4-8) reveal that best control strategies for malaria elimination is the combination of ITN, Chemoprophylaxis and Improved Clinical Treatment. However, the Cost-effectiveness Analysis points out that ITN is economically best solution for fighting malaria in poor malaria endemic areas.

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