Analyzing Behavioural Pattern of Malware Propagation in Mobile Environment

2020 ◽  
Vol 17 (5) ◽  
pp. 2125-2129
Author(s):  
G. Maria Jones ◽  
S. Godfrey Winster
Keyword(s):  
Equilibrium State ◽  
Dynamical Behavior ◽  
Propagation Model ◽  
Basic Reproductive Number ◽  
Smart Devices ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Mobile Environment ◽  
Single Node ◽  
Malware Propagation

The evolution of mobile devices technology has no longer novelty but the usage of the device has been different from persons to persons with variety of purposes. Due to their compatibility in size and portability, the smart devices are prone to attack. Once a single node of the mobile network is attacked, it can compromise the entire network. In this paper, a study of malware attacking behavior is done and used fractional discrete model to analysis the attacking and spreading behavior of possible malware in mobile environment is examined. The mobile malware propagation model is analyzed, and investigated using the stability theory and also proposed a model S (Susceptible state), L (Latent state) and B (Breaking state). Here, basic reproductive number helps to analysis the malware propagation which helps us to find the threshold values. If the reproduction number is less than one, then the malware free equilibrium state is locally asymptotically stable. Endemic equilibrium state is globally asymptotically stable if reproductive number greater than one. Numerical illustrations assure the consistency of the theoretical analysis and interesting dynamical behavior of the system is observed.

scholarly journals Modeling and Analysis of the Spread of Malware with the Influence of User Awareness

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Qingyi Zhu ◽  
Xuhang Luo ◽  
Yuhang Liu
Keyword(s):  
Propagation Model ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Sis Model ◽  
Globally Asymptotically Stable ◽  
Modeling And Analysis ◽  
Malware Propagation ◽  
User Awareness

By incorporating the security awareness of computer users into the susceptible-infected-susceptible (SIS) model, this study proposes a new malware propagation model, named the SID model, where D compartment denotes the group of nodes with user awareness. Through qualitative analysis, the basic reproductive number R 0 is given. Furthermore, it is proved that the virus-free equilibrium is globally asymptotically stable if R 0 is less than one, whereas the viral equilibrium is globally asymptotically stable if R 0 is greater than one. Then, some numerical examples are given to demonstrate the analytical results. Finally, we put forward some efficient control measures according to the theoretical and experimental analysis.

scholarly journals Dynamical Behavior of a New Epidemiological Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zizi Wang ◽  
Zhiming Guo
Keyword(s):  
Time Delay ◽  
Dynamical Behavior ◽  
Endemic Equilibrium ◽  
Epidemiological Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain timeτ. The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive numberR0is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease-free equilibrium is globally asymptotically stable provided thatR0≤1; ifR0>1, then there exists a unique endemic equilibrium, and it is globally asymptotically stable. For the model with time delay, a sufficient condition is given to ensure that the disease-free equilibrium is locally asymptotically stable. Hopf bifurcation in endemic equilibrium with respect to the timeτis also addressed.

scholarly journals Malware propagation model for cluster-based wireless sensor networks using epidemiological theory

2021 ◽  
Vol 7 ◽  
pp. e728
Author(s):  
Xuejin Zhu ◽  
Jie Huang
Keyword(s):  
Propagation Model ◽  
Sensor Nodes ◽  
Basic Reproductive Number ◽  
Wireless Sensor ◽  
Reproductive Number ◽  
Defense Strategies ◽  
Actual Application ◽  
Malware Propagation ◽  
Mixed Strategy Nash Equilibrium ◽  
Attack And Defense

Due to limited resources, wireless sensor network (WSN) nodes generally possess weak defense capabilities and are often the target of malware attacks. Attackers can capture or infect specific sensor nodes and propagate malware to other sensor nodes in WSNs through node communication. This can eventually infect an entire network system and even cause paralysis. Based on epidemiological theory, the present study proposes a malware propagation model suitable for cluster-based WSNs to analyze the propagation dynamic of malware. The model focuses on the data-transmission characteristics between different nodes in a cluster-based network and considers the actual application parameters of WSNs, such as node communication radius, node distributed density, and node death rate. In addition, an attack and defense game between malware and defending systems is also established, and the infection and recovery rates of malware propagation under the mixed strategy Nash equilibrium condition are given. In particular, the basic reproductive number, equilibrium point, and stability of the model are derived. These studies revealed that a basic reproductive number of less than 1 leads to eventual disappearance of malware, which provides significant insight into the design of defense strategies against malware threats. Numerical experiments were conducted to validate the theory proposed, and the influence of WSN parameters on malware propagation was examined.

scholarly journals On the Optimal Control of a Malware Propagation Model

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1518
Author(s):  
Jose Diamantino Hernández Guillén ◽  
Ángel Martín del Rey ◽  
Roberto Casado Vara
Keyword(s):  
Optimal Control ◽  
Control Measure ◽  
Propagation Model ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Security Measures ◽  
Epidemic Process ◽  
Malware Propagation ◽  
Prevention Measure

An important way considered to control malware epidemic processes is to take into account security measures that are associated to the systems of ordinary differential equations that governs the dynamics of such systems. We can observe two types of control measures: the analysis of the basic reproductive number and the study of control measure functions. The first one is taken at the beginning of the epidemic process and, therefore, we can consider this to be a prevention measure. The second one is taken during the epidemic process. In this work, we use the theory of optimal control that is associated to systems of ordinary equations in order to find a new function to control malware epidemic through time. Specifically, this approach is evaluate on a particular compartmental malware model that considers carrier devices.

Global properties for an age-structured within-host model with Crowley–Martin functional response

2017 ◽  
Vol 10 (02) ◽  
pp. 1750030 ◽  
Author(s):  
Shaoli Wang ◽  
Xinyu Song
Keyword(s):  
Functional Response ◽  
Viral Infections ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Multi Scale ◽  
Global Properties ◽  
Age Structured

Based on a multi-scale view, in this paper, we study an age-structured within-host model with Crowley–Martin functional response for the control of viral infections. By means of semigroup and Lyapunov function, the global asymptotical property of infected steady state of the model is obtained. The results show that when the basic reproductive number falls below unity, the infection dies out. However, when the basic reproductive number exceeds unity, there exists a unique positive equilibrium which is globally asymptotically stable. This model can be deduced to different viral models with or without time delay.

scholarly journals Global Stability of an SEIS Epidemic Model with General Saturation Incidence

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hui Zhang ◽  
Li Yingqi ◽  
Wenxiong Xu
Keyword(s):  
Latent Period ◽  
Epidemic Model ◽  
Convergence Theorem ◽  
Incidence Rates ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

We present an SEIS epidemic model with infective force in both latent period and infected period, which has different general saturation incidence rates. It is shown that the global dynamics are completely determined by the basic reproductive number R0. If R0≤1, the disease-free equilibrium is globally asymptotically stable in T by LaSalle’s Invariance Principle, and the disease dies out. Moreover, using the method of autonomous convergence theorem, we obtain that the unique epidemic equilibrium is globally asymptotically stable in T0, and the disease spreads to be endemic.

scholarly journals Global Dynamics of an HTLV-1 Model with Cell-to-Cell Infection and Mitosis

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Sumei Li ◽  
Yicang Zhou
Keyword(s):  
Chronic Infection ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Cell Infection ◽  
Globally Asymptotically Stable ◽  
Human T Cell

A mathematical model of human T-cell lymphotropic virus type 1 in vivo with cell-to-cell infection and mitosis is formulated and studied. The basic reproductive numberR0is derived. It is proved that the dynamics of the model can be determined completely by the magnitude ofR0. The infection-free equilibrium is globally asymptotically stable (unstable) ifR0<1  (R0>1). There exists a chronic infection equilibrium and it is globally asymptotically stable ifR0>1.

scholarly journals Mathematical Analysis A Continuous Vaccination Strategy Effect against to spread of Measles by Using the Epidemic SVIR Models

2017 ◽  
Author(s):  
Tonaas Kabul Wangkok Yohanis Marentek
Keyword(s):  
Fixed Point ◽  
Vaccination Strategy ◽  
Fixed Time ◽  
Basic Reproductive Number ◽  
Necessary Condition ◽  
Reproductive Number ◽  
Time Interval ◽  
Asymptotically Stable ◽  
Fixed Time Interval ◽  
Disease Free

Vaccination is one way to minimize the spread of disease. To complete a vaccination, it is usually done several times and there should be a fixed time interval. Considering vaccination in the basic SIR model, SVIR model assumes that individuals are vaccinated do not get immediate immunity means that individuals who are vaccinated still allow infected. So according to the process of vaccination on SVIR model, there are two strategies which continuous vaccination strategy (CVS) and disconnected vaccination strategy (PVS). In this study only addressed continuous vaccination strategy in epidemic model SVIR. Results from the study indicate that the dynamics of the CVS system is fully dependent on the basic reproductive number. If the basic reproductive number is less than one then the fixed point asymptotically stable disease-free will which means that eventually the disease will disappear from the population. Conversely, if more than one fixed point is asymptotically stable endemic would mean that the disease will still exist in the population. Mathematical results show that vaccination helps to minimize the spread of disease by reducing the basic reproductive number. But there is a necessary condition for the disease can be eradicated. If the time for the vaccine recipients to obtain immunity or the possibility of vaccine recipients infected neglected, the condition of the disease will disappear and the disease will always be eradicated. This can lead to over-evaluating the effect of vaccination.

SVIR epidemic model with age structure in susceptibility, vaccination effects and relapse

2017 ◽  
Vol 82 (5) ◽  
pp. 945-970 ◽  
Author(s):  
Jinliang Wang ◽  
Min Guo ◽  
Shengqiang Liu
Keyword(s):  
Age Structure ◽  
Epidemic Model ◽  
Lyapunov Functional ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Combined Effects ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Disease Free

Abstract An SVIR epidemic model with continuous age structure in the susceptibility, vaccination effects and relapse is proposed. The asymptotic smoothness, existence of a global attractor, the stability of equilibria and persistence are addressed. It is shown that if the basic reproductive number $\Re_0&lt;1$, then the disease-free equilibrium is globally asymptotically stable. If $\Re_0&gt;1$, the disease is uniformly persistent, and a Lyapunov functional is used to show that the unique endemic equilibrium is globally asymptotically stable. Combined effects of susceptibility age, vaccination age and relapse age on the basic reproductive number are discussed.

SCIR rumor propagation model with the chord mechanism in social networks

2021 ◽  
pp. 2250014
Author(s):  
Zhou Xiaodan ◽  
Qiu Liqing ◽  
Hao Tingyu
Keyword(s):  
Negative Impact ◽  
Real Life ◽  
Propagation Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Essential Difference ◽  
Social Phenomenon ◽  
Rumor Propagation ◽  
Number Formula ◽  
Next Generation Matrix

Rumors, as a typical social phenomenon in real life, have a negative impact on the harmony of the society. When people hear rumors, they may not resonate with rumors because they do not trust them during the process of rumors transmission. Thus, they will not spread rumors. The essential difference between chord mechanism and spreader mechanism is that spreaders will spread regardless of whether they think it is true or false. The chord needs to believe that the rumor is true in order to keep spreading it, otherwise they become immune to spreading it. Therefore, this paper proposes a new Spreader-Chord-Ignorant-Restorer (SCIR) model, which considers that the trust may affect the level of empathy. Since the level of trust affects the spread of rumors and the extent to which the immune person trusts the rumor is different, the connecting edges from the restorer to the chord and the restorer to the ignorant were added to the model. First, the basic reproductive number [Formula: see text] is derived by the next generation matrix method and thus equilibriums are obtained. Then, the global stability of the rumor-free equilibrium [Formula: see text] and the persistence of rumor propagation are proved in detail during the theoretical analysis.

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