Behavioral Modeling of Malicious Objects in a Highly Infected Network Under Quarantine Defence

2019 ◽  
Vol 13 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Yerra Shankar Rao ◽  
Prasant Kumar Nayak ◽  
Hemraj Saini ◽  
Tarini Charana Panda
Keyword(s):  
Control Strategy ◽  
Computer Network ◽  
Reproduction Number ◽  
Malicious Code ◽  
Behavioral Modeling ◽  
Asymptotically Stable ◽  
Matlab Simulation ◽  
Safety Measures ◽  
Malicious Codes ◽  
The Stability

This article describes a highly infected e-epidemic model in a computer network. This article establishes the Basic reproduction number R0, which explicitly brings out the stability conditions. Further, the article shows that if R0< 1 then the infected nodes ceases the spreading of malicious code in computer network as it dies down and consequently establishes the asymptotically stable, when R0> 1, the alternative aspect is that infected nodes stretch out into the network and becomes asymptotically unstable. The pivotal, impact of quarantine node on e-epidemic models has been verified along with its control strategy for a high infected computer network. In the MATLAB simulation, the quarantine class shows its explicit relationship with respect to high as well as low infected class, exposed class, and finally, with recovery class in order to yield increasing safety measures on transmission of malicious codes.

Mathematical Model for Cyber Attack in Computer Network

2017 ◽  
Vol 13 (1) ◽  
pp. 58-65 ◽  
Author(s):  
Yerra Shankar Rao ◽  
Aswin Kumar Rauta ◽  
Hemraj Saini ◽  
Tarini Charana Panda
Keyword(s):  
Computer Network ◽  
Real Life ◽  
Threshold Value ◽  
Malicious Code ◽  
Threshold Condition ◽  
Asymptotically Stable ◽  
Cyber Attack ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Fifth Order

This investigation focuses to develop an e-SEIRS (susceptible, exposed, infectious, recovered) epidemic computer network model to study the transmission of malicious code in a computer network and derive the approximate threshold condition (basic reproduction number) to examine the equilibrium and stability of the model. The authors have simulated the results for various parameters used in the model and Runge-Kutta Fehlberg fourth-fifth order method is employed to solve system of equations developed. They have studied the stability of crime level to equilibrium and found the critical value of threshold value determining whether or not the infectious free equilibrium is globally asymptotically stable and endemic equilibrium is locally asymptotically stable. The simulation results using MATLAB agree with the real life situations.

scholarly journals Simple MSEIR Model for Measles Transmission

2019 ◽  
pp. 1-11
Author(s):  
Mojeeb Al-Rahman EL-Nor Osman ◽  
Appiagyei Ebenezer ◽  
Isaac Kwasi Adu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Birth Rate ◽  
Reproduction Number ◽  
Progression Rate ◽  
Asymptotically Stable ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an Immunity-Susceptible-Exposed-Infectious-Recovery (MSEIR) mathematical model was used to study the dynamics of measles transmission. We discussed that there exist a disease-free and an endemic equilibria. We also discussed the stability of both disease-free and endemic equilibria.  The basic reproduction number  is obtained. If , then the measles will spread and persist in the population. If , then the disease will die out.  The disease was locally asymptotically stable if  and unstable if  . ALSO, WE PROVED THE GLOBAL STABILITY FOR THE DISEASE-FREE EQUILIBRIUM USING LASSALLE'S INVARIANCE PRINCIPLE OF Lyaponuv function. Furthermore, the endemic equilibrium was locally asymptotically stable if , under certain conditions. Numerical simulations were conducted to confirm our analytic results. Our findings were that, increasing the birth rate of humans, decreasing the progression rate, increasing the recovery rate and reducing the infectious rate can be useful in controlling and combating the measles.

scholarly journals Mathematical analysis of an age structured epidemic model with a quarantine class

2021 ◽  
Author(s):  
Bedreddine AINSEBA ◽  
Tarik Touaoula ◽  
Zakia Sari
Keyword(s):  
Reproduction Number ◽  
Asymptotic Behavior Of Solutions ◽  
Model Parameters ◽  
Qualitative Behavior ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
The Stability ◽  
The Impact

In this paper, an age structured epidemic Susceptible-Infected-Quarantined-Recovered-Infected (SIQRI) model is proposed, where we will focus on the role of individuals that leave their class of quarantine before being completely recovered and thus will participate again to the transmission of the disease. We investigate the asymptotic behavior of solutions by studying the stability of both trivial and positive equilibria. In order to see the impact of the different model parameters like the relapse rate on the qualitative behavior of our system, we firstly, give the explicit expression of the epidemic reproduction number $R_{0}.$ This number is a combination of the classical epidemic reproduction number for the SIQR model and a new epidemic reproduction number corresponding to the individuals infected by a relapsed person from the R-class. It is shown that, if $R_{0}\leq 1$, the disease free equilibrium is globally asymptotically stable and becomes unstable for $R_{0}>1$. Secondly, while $R_{0}>1$, a suitable Lyapunov functional is constructed to prove that the unique endemic equilibrium is globally asymptotically stable on some subset $\Omega_{0}.$

scholarly journals Drug-sensitivity and passive immunity mathematical epidemiological model for tuberculosis

2021 ◽  
Vol 25 (9) ◽  
pp. 1661-1670
Author(s):  
A.A. Danhausa ◽  
E.E. Daniel ◽  
C.J. Shawulu ◽  
A.M. Nuhu ◽  
L. Philemon
Keyword(s):  
Control Strategy ◽  
Drug Sensitivity ◽  
Reproduction Number ◽  
Passive Immunity ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Latently Infected ◽  
Widespread Availability ◽  
Next Generation Matrix ◽  
Disease Free

Regardless of many decades of research, the widespread availability of a vaccine and more recently highly visible WHO efforts to promote a unified global control strategy, Tuberculosis remains a leading cause of infectious mortality. In this paper, a Mathematical Model for Tuberculosis Epidemic with Passive Immunity and Drug-Sensitivity is presented. We carried out analytical studies of the model where the population comprises of eight compartments: passively immune infants, susceptible, latently infected with DS-TB. The Disease Free Equilibrium (DFE) and the Endemic Equilibrium (EE) points were established. The next generation matrix method was used to obtain the reproduction number for drug sensitive (𝑅𝑜𝑠) Tuberculosis. We obtained the disease-free equilibrium for drug sensitive TB which is locally asymptotically stable when 𝑅𝑜𝑠 < 1 indicating that tuberculosis eradication is possible within the population. We also obtained the global stability of the disease-free equilibrium and results showed that the disease-free equilibrium point is globally asymptotically stable when 𝑅𝑜𝑠 ≤ 1 which indicates that tuberculosis naturally dies out.

scholarly journals Analisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Penyakit Ebola dengan Penanganan Medis

2019 ◽  
Vol 1 (1) ◽  
pp. 19
Author(s):  
Sofita Suherman ◽  
Fatmawati Fatmawati ◽  
Cicik Alfiniyah
Keyword(s):  
Optimal Control ◽  
Medical Treatment ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
The Stability ◽  
The Mathematical Model ◽  
Treatment Population ◽  
Deceased Individual ◽  
Two Equilibria

Ebola disease is one of an infectious disease caused by a virus. Ebola disease can be transmitted through direct contact with Ebola’s patient, infected medical equipment, and contact with the deceased individual. The purpose of this paper is to analyze the stability of equilibriums and to apply the optimal control of treatment on the mathematical model of the spread of Ebola with medical treatment. Model without control has two equilibria, namely non-endemic equilibrium (E0) and endemic equilibrium (E1) The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is locally asymptotically stable if  R0 < 1 and endemic equilibrium tend to asymptotically stable if R0 >1 . The problem of optimal control is then solved by Pontryagin’s Maximum Principle. From the numerical simulation result, it is found that the control is effective to minimize the number of the infected human population and the number of the infected human with medical treatment population compare without control.

scholarly journals Analisis kestabilan dan kontrol optimal model matematika penyebaran penyakit Ebola dengan variabel kontrol berupa karantina

2021 ◽  
Vol 2 (1) ◽  
pp. 29-41
Author(s):  
Erzalina Ayu Satya Megananda ◽  
Cicik Alfiniyah ◽  
Miswanto Miswanto
Keyword(s):  
Optimal Control ◽  
Human Population ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Optimal Model ◽  
The Family ◽  
The Stability ◽  
The Cost ◽  
Two Equilibria

Ebola disease is an infectious disease caused by a virus from the genus Ebolavirus and the family Filoviridae. Ebola disease is one of the most deadly diseases for human. The purpose of the thesis is to analyze the stability of the equilibrium point and to apply the optimal control of quarantine on a mathematical model of the spread of ebola. Model without control has two equilibria, non-endemic equilibrium and endemic equilibrium. The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is asymptotically stable if R0 1 and endemic equilibrium tend to asymptotically stable if R0 1. The problem of optimal control is solved by Pontryagin’s Maximum Principle. From the numerical simulation, the result shows that control is effective enough to minimize the number of infected human population and to minimize the cost of its control.

scholarly journals Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Bouchaib Khajji ◽  
Abderrahim Labzai ◽  
Omar Balatif ◽  
Mostafa Rachik
Keyword(s):  
Alcohol Drinking ◽  
Addiction Treatment ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Modeling And Analysis ◽  
Private And Public ◽  
The Stability

In this paper, we present a continuous mathematical model PMHTrTpQ of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number R0. We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number R0. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium E0 when R0≤1. When R0>1, drinking present equilibrium E∗ exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium E∗.

scholarly journals On Oscillatory Pattern of Malaria Dynamics in a Population with Temporary Immunity

2007 ◽  
Vol 8 (3) ◽  
pp. 191-203 ◽  
Author(s):  
J. Tumwiine ◽  
J. Y. T. Mugisha ◽  
L. S. Luboobi
Keyword(s):  
Steady State ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Oscillatory Pattern ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number ◽  
Temporary Immunity

We use a model to study the dynamics of malaria in the human and mosquito population to explain the stability patterns of malaria. The model results show that the disease-free equilibrium is globally asymptotically stable and occurs whenever the basic reproduction number,R0is less than unity. We also note that whenR0>1, the disease-free equilibrium is unstable and the endemic equilibrium is stable. Numerical simulations show that recoveries and temporary immunity keep the populations at oscillation patterns and eventually converge to a steady state.

STABILITY OF AN AGE-STRUCTURED SEIS EPIDEMIC MODEL WITH INFECTIVITY IN INCUBATIVE PERIOD

2010 ◽  
Vol 03 (03) ◽  
pp. 299-312 ◽  
Author(s):  
SHU-MIN GUO ◽  
XUE-ZHI LI ◽  
XIN-YU SONG
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Stability Conditions ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an age-structured SEIS epidemic model with infectivity in incubative period is formulated and studied. The explicit expression of the basic reproduction number R0 is obtained. It is shown that the disease-free equilibrium is globally asymptotically stable if R0 < 1, at least one endemic equilibrium exists if R0 > 1. The stability conditions of endemic equilibrium are also given.

The Research of Malicious Code's Spread and Found Technology

2013 ◽  
Vol 860-863 ◽  
pp. 2750-2753
Author(s):  
Ya Qin Fan ◽  
Xin Zhang ◽  
Xin Yu Chen ◽  
Chi Li
Keyword(s):  
Simulation Software ◽  
Malicious Code ◽  
Propagation Model ◽  
Matlab Simulation ◽  
Malware Propagation ◽  
Detection Technology ◽  
Malicious Codes ◽  
Improved Methods

In order to defense malicious codes increasing serious infestations actively. We proposed several corresponding malicious code found and detection technology on the basis of malware propagation principle. We use MATLAB simulation software to achieve the malware propagation model and detection technology. We proved the practicability of the discovery technology, and present improved methods for the deficiency of the model.

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