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 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 Prevention of Influenza Pandemic by Multiple Control Strategies

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Roman Ullah ◽  
Gul Zaman ◽  
Saeed Islam
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Antiviral Treatment ◽  
Cost Effective ◽  
Effective Control ◽  
Numerical Techniques ◽  
Multiple Control ◽  
Control Functions ◽  
Transmission Of Disease

We present the prevention of influenza pandemic by using multiple control functions. First, we adjust the control functions in the pandemic model, then we show the existence of the optimal control problem, and, by using both analytical and numerical techniques, we investigate cost-effective control effects for the prevention of transmission of disease. To do this, we use four control functions, the first one for increasing the effect of vaccination, the second one for the strategies to isolate infected individuals, and the last two for the antiviral treatment to control clinically infectious and hospitalization cases, respectively. We completely characterized the optimal control and compute the numerical solution of the optimality system by using an iterative method.

scholarly journals State-Based Switching for Optimal Control of Computer Virus Propagation with External Device Blocking

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Qingyi Zhu ◽  
Seng W. Loke ◽  
Ye Zhang
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Minimum Principle ◽  
Optimal Solution ◽  
Computer Virus ◽  
Numerical Results ◽  
Difference Approximation ◽  
External Device ◽  
Virus Propagation ◽  
The Impact

The rapid propagation of computer virus is one of the greatest threats to current cybersecurity. This work deals with the optimal control problem of virus propagation among computers and external devices. To formulate this problem, two control strategies are introduced: (a) external device blocking, which means prohibiting a fraction of connections between external devices and computers, and (b) computer reconstruction, which includes updating or reinstalling of some infected computers. Then the combination of both the impact of infection and the cost of controls is minimized. In contrast with previous works, this paper takes into account a state-based cost weight index in the objection function instead of a fixed one. By using Pontryagin’s minimum principle and a modified forward-backward difference approximation algorithm, the optimal solution of the system is investigated and numerically solved. Then numerical results show the flexibility of proposed approach compared to the regular optimal control. More numerical results are also given to evaluate the performance of our approach with respect to various weight indexes.

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 Optimization of the Controls against the Spread of Zika Virus in Populations

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 76
Author(s):  
Gilberto González-Parra ◽  
Miguel Díaz-Rodríguez ◽  
Abraham J. Arenas
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Zika Virus ◽  
Control Strategies ◽  
Real Life ◽  
Real Data ◽  
Control Measures ◽  
Information Campaigns ◽  
Control Functions ◽  
Cost Efficient

In this paper, we study and explore two control strategies to decrease the spread of Zika virus in the human and mosquito populations. The control strategies that we consider in this study are awareness and spraying campaigns. We solve several optimal control problems relying on a mathematical epidemic model of Zika that considers both human and mosquito populations. The first control strategy is broad and includes using information campaigns, encouraging people to use bednetting, wear long-sleeve shirts, or similar protection actions. The second control is more specific and relies on spraying insecticides. The control system relies on a Zika mathematical model with control functions. To develop the optimal control problem, we use Pontryagins’ maximum principle, which is numerically solved as a boundary value problem. For the mathematical model of the Zika epidemic, we use parameter values extracted from real data from an outbreak in Colombia. We study the effect of the costs related to the controls and infected populations. These costs are important in real life since they can change the outcomes and recommendations for health authorities dramatically. Finally, we explore different options regarding which control measures are more cost-efficient for society.

scholarly journals On the Optimal Dynamic Control Strategy of Disruptive Computer Virus

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Jichao Bi ◽  
Xiaofan Yang ◽  
Yingbo Wu ◽  
Qingyu Xiong ◽  
Junhao Wen ◽  
...  
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Control Strategies ◽  
Dynamic Control ◽  
Cost Effective ◽  
Computer Virus ◽  
Economic Losses ◽  
Computer Viruses ◽  
Effective Dynamic ◽  
Optimal Dynamic

Disruptive computer viruses have inflicted huge economic losses. This paper addresses the development of a cost-effective dynamic control strategy of disruptive viruses. First, the development problem is modeled as an optimal control problem. Second, a criterion for the existence of an optimal control is given. Third, the optimality system is derived. Next, some examples of the optimal dynamic control strategy are presented. Finally, the performance of actual dynamic control strategies is evaluated.

scholarly journals The co-dynamics of Hepatitis E and HIV

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4723-4745
Author(s):  
Ebraheem Alzahrani ◽  
Muhammad Khan
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Bifurcation Analysis ◽  
Disease Burden ◽  
Control Strategies ◽  
Hepatitis E ◽  
Control Model ◽  
Full Model ◽  
Dynamics Model ◽  
Infection Dynamics

This work investigates the co-dynamics of Hepatitis E and HIV. Initially, we formulate a co-infection dynamics model of Hepatitis E and HIV. Then, we analyze each model and discuss their mathematical results. After that, we investigate the full model and present their basic mathematical results. A bifurcation analysis for full model is investigated. Further, we formulate a mathematical model with five controls. Optimal control model is formulated and the necessary results of the optimal control characterization are presented. Moreover, numerical results with different control strategies are presented. It is shown that each strategy has its own importance but for the disease elimination the combination of all the five controls at the same time can best decrease the disease burden from the community.

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 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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