scholarly journals Analysis of a Model for Computer Virus Transmission

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Peng Qin
Keyword(s):  
Theoretical Basis ◽  
Computer Network ◽  
Equilibrium Points ◽  
Virus Transmission ◽  
Computer Virus ◽  
Stability Conditions ◽  
Computer Viruses ◽  
Virus Model ◽  
The Stability ◽  
Disease Free

Computer viruses remain a significant threat to computer networks. In this paper, the incorporation of new computers to the network and the removing of old computers from the network are considered. Meanwhile, the computers are equipped with antivirus software on the computer network. The computer virus model is established. Through the analysis of the model, disease-free and endemic equilibrium points are calculated. The stability conditions of the equilibria are derived. To illustrate our theoretical analysis, some numerical simulations are also included. The results provide a theoretical basis to control the spread of computer virus.

Stability Analysis of Computer Virus Model System in Networks

2013 ◽  
Vol 278-280 ◽  
pp. 2033-2038 ◽  
Author(s):  
Shao Ting Ge ◽  
Gong You Tang ◽  
Xue Yang ◽  
Qi Lei Xu ◽  
Hao Yu ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Computer Virus ◽  
Model System ◽  
Virus Model ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Mathematical Model ◽  
Disease Free

This paper considers stability analysis of a discrete-time computer virus model in networks. The disease-free equilibrium and the disease equilibrium are first derived from the mathematical model. Then the sufficient condition of stability for the disease-free equilibrium is obtained by the first Lyapunov method. And the sufficient conditions of stability for the disease equilibrium are given by disc theorem. Simulation results demonstrate the effectiveness of the stability conditions.

scholarly journals Bifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network

2021 ◽  
Vol 19 (2) ◽  
pp. 1677-1695
Author(s):  
Boli Xie ◽  
◽  
Maoxing Liu ◽  
Lei Zhang
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Virus Transmission ◽  
Population Heterogeneity ◽  
Multiple Equilibrium ◽  
Optimal Control Strategy ◽  
Treatment Function ◽  
The Stability ◽  
The Impact

<abstract><p>In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that $ R_{0} &lt; 1 $ is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near $ R_{0} = 1 $. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.</p></abstract>

scholarly journals Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

2020 ◽  
Author(s):  
Tamer Sanlidag ◽  
Nazife Sultanoglu ◽  
Bilgen Kaymakamzade ◽  
Evren Hincal ◽  
Murat Sayan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Real Data ◽  
Northern Cyprus ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstract The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2 epidemic.

scholarly journals Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

2020 ◽  
Author(s):  
Tamer Sanlidag ◽  
Nazife Sultanoglu ◽  
Bilgen Kaymakamzade ◽  
Evren Hincal ◽  
Murat Sayan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Real Data ◽  
Northern Cyprus ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstract The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2epidemic.

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.

scholarly journals A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahram Rezapour ◽  
Hakimeh Mohammadi
Keyword(s):  
Fractional Order ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Point Theory ◽  
Euler Method ◽  
Transmission Model ◽  
Order Model ◽  
Influenza Transmission ◽  
The Stability ◽  
Disease Free

Abstract We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stability of the disease-free equilibrium point is investigated. We prove the existence of solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. In the numerical section, we present a simulation to examine the system, in which we calculate equilibrium points of the system and examine the behavior of the resulting functions at the equilibrium points. By calculating the results of the model for different fractional order, we examine the effect of the derivative order on the behavior of the resulting functions and obtained numerical values. We also calculate the results of the integer-order model and examine their differences with the results of the fractional-order model.

scholarly journals Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina

2021 ◽  
Author(s):  
Resmawan Resmawan ◽  
Agusyarif Rezka Nuha ◽  
Lailany Yahya
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Human Class ◽  
Existence Of Equilibrium ◽  
The Stability ◽  
Disease Free

This paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R0&lt;1 and unstable at R0&gt;1. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.

scholarly journals Mathematical Analysis of a Diarrhoea Model in the Presence of Vaccination and Treatment Waves with Sensitivity Analysis

2021 ◽  
Vol 25 (7) ◽  
pp. 1107-1114
Author(s):  
E.I. Akinola ◽  
B.E. Awoyemi ◽  
I.A. Olopade ◽  
O.D. Falowo ◽  
T.O. Akinwumi
Keyword(s):  
Sensitivity Analysis ◽  
Mathematical Analysis ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Runge Kutta Method ◽  
Modelling Techniques ◽  
Uniqueness And Existence ◽  
The Stability ◽  
Order Four ◽  
Disease Free

In this study, the diarrhoea model is developed based on basic mathematical modelling techniques leading to a system (five compartmental model) of ordinary differential equations (ODEs). Mathematical analysis of the model is then carried out on the uniqueness and existence of the model to know the region where the model is epidemiologically feasible. The equilibrium points of the model and the stability of the disease-free state were also derived by finding the reproduction number. We then progressed to running a global sensitivity analysis on the reproduction number with respect to all the parameters in it, and four (4) parameters were found sensitive. The work was concluded with numerical simulations on Maple 18 using Runge-Kutta method of order four (4) where the values of six (6) parameters present in the model were each varied successively while all other parameters were held constant so as to know the behaviour and effect of the varied parameter on how diarrhoea spreads in the population. The results from the sensitivity analysis and simulations were found to be in sync.

scholarly journals Analisis Kestabilan Model Host-Vector Transmisi HIV/AIDS Pada Pengguna Jarum Suntik

2017 ◽  
Vol 7 (1) ◽  
pp. 1
Author(s):  
Jafaruddin (Alm) ◽  
Rapmaida M. Pangaribuan ◽  
. Aryanto ◽  
Irena A. Henukh
Keyword(s):  
Sensitivity Analysis ◽  
Equilibrium Point ◽  
Drug Users ◽  
Endemic Equilibrium ◽  
Vector Model ◽  
Stability Conditions ◽  
Keywords Hiv ◽  
The Stability ◽  
Disease Free ◽  
Hiv Aids

HIV/AIDS is a very dangerous disease. The transmission of  HIV/AIDS can be in three ways  and one of them through a syringe. In this paper we describe SIR and SEIR Host-Vector  model transmission of HIV/AIDS amongst populations of  injecting drug users. From the existing model we obtained disease-free equilibrium  point and endemic equilibrium point. Then we study the stability conditions and sensitivity analysis of the  . The analysis shows if   then the disease-free equilibrium  point is stable and if    then the endemic equilibrium point will be stable. We also obtained that parameter of probality host-vector infected with HIV/AIDS affects the increase of  number  infected HIV/AIDS. Keywords: HIV/AIDS, Host-Vector Transmission, The Stability of Equilibrium Point.

scholarly journals Analisis Kestabilan Model SEIR Penyebaran Penyakit Campak dengan Pengaruh Imunisasi dan Vaksin MR

2019 ◽  
Vol 16 (1) ◽  
pp. 107
Author(s):  
Willyam Daniel Sihotang ◽  
Ceria Clara Simbolon ◽  
July Hartiny ◽  
Desrinawati Tindaon ◽  
Lasker Pangarapan Sinaga
Keyword(s):  
Infectious Disease ◽  
Equilibrium Point ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Seir Model ◽  
Rate Of Spread ◽  
The Stability ◽  
Disease Free

Measles is a contagious infectious disease caused by a virus and has the potential to cause an outbreak. Immunization and vaccination are carried out as an effort to prevent the spread of measles. This study aims to analyze and determine the stability of the SEIR model on the spread of measles with the influence of immunization and MR vaccines. The results obtained from model analysis, namely there are two disease free and endemic equilibrium points. If the conditions are met, the measles-free equilibrium point will be asymptotically stable and the measles endemic equilibrium point will be stable. Numerical solutions show a decrease in the rate of spread of measles due to the effect of immunization and the addition of MR vaccines.

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