Parameter estimation of a susceptible–infected–recovered–dead computer worm model

SIMULATION ◽  
2021 ◽  
pp. 003754972110095
Author(s):  
Yue Deng ◽  
Yongzhen Pei ◽  
Changguo Li
Keyword(s):  
Parameter Estimation ◽  
Equation Model ◽  
Internet Security ◽  
Economic Losses ◽  
Unknown Parameters ◽  
Differential Equation Model ◽  
Computer Worms ◽  
Computer Worm ◽  
Worm Model ◽  
Ensemble Kalman Filtering

Computer worms are serious threats to Internet security and have caused billions of dollars of economic losses during the past decades. In this study, we implemented a susceptible–infected–recovered–dead (SIRD) model of computer worms and analyzed the characteristics and mechanisms of worm transmission. We applied the ordinary differential equation model to simulate the transmission process of computer worms and estimated the unknown parameters of the SIRD model through the methods of least squares, Markov chain Monte Carlo, and ensemble Kalman filtering (ENKF). The results reveal that the proposed SIRD model is more accurate than the susceptible–exposed–infected–recovered–susceptible model with respect to parameter estimation.

Parametric Identification of an Experimental Two-Well Oscillator

1999 ◽  
Author(s):  
B. F. Feeny ◽  
C.-M. Yuan
Keyword(s):  
Periodic Orbits ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Parametric Identification ◽  
Equation Model ◽  
Unknown Parameters ◽  
Differential Equation Model ◽  
Identification Process ◽  
Nonlinear Force ◽  
Force Displacement

Abstract The identification of parameters in an experimental two-well chaotic system is presented. The method involves the extraction of periodic orbits from a chaotic set. The form of the differential-equation model is assumed, with unknown coefficients on the terms in the model. The harmonic-balance method is applied to these periodic orbits, resulting in a linear equation in the unknown parameters, which can then be solved in the least-squares sense. The identification process reveals the nonlinear force-displacement characteristic of the oscillator. The results are cross-checked with various sets of extracted periodic orbits. The model is validated by examining simulated responses.

scholarly journals Evaluation of the Number of Visits to Chinese Medical Institutions Using a Logistic Differential Equation Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Xiaoxia Zhao ◽  
Wei Li ◽  
Yanyang Wang ◽  
Lihong Jiang
Keyword(s):  
Differential Equation ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Equation Model ◽  
Positive Equilibrium ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Differential Equation Model ◽  
Number Of Visits ◽  
Positive Equilibrium Point

In this study, we established a two-dimensional logistic differential equation model to study the number of visits in Chinese PHCIs and hospitals based on the behavior of patients. We determine the model's equilibrium points and analyze their stability and then use China medical services data to fit the unknown parameters of the model. Finally, the sensitivity of model parameters is evaluated to determine the parameters that are susceptible to influence the system. The results indicate that the system corresponds to the zero-equilibrium point, the boundary equilibrium point, and the positive equilibrium point under different parameter conditions. We found that, in order to substantially increase visits to PHCIs, efforts should be made to improve PHCI comprehensive capacity and maximum service capacity.

scholarly journals A spatially varying stochastic differential equation model for animal movement

2018 ◽  
Vol 12 (2) ◽  
pp. 1312-1331 ◽  
Author(s):  
James C. Russell ◽  
Ephraim M. Hanks ◽  
Murali Haran ◽  
David Hughes
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Animal Movement ◽  
Equation Model ◽  
Differential Equation Model ◽  
Spatially Varying

scholarly journals A Stochastic TB Model for a Crowded Environment

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Sibaliwe Maku Vyambwera ◽  
Peter Witbooi
Keyword(s):  
Compartmental Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Equation Model ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
The Stability ◽  
Crowded Environments ◽  
Disease Free

We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease-free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability of the disease-free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.

Time Fractional Differential Equation Model With Random Derivative Order

2009 ◽  
Author(s):  
Hongguang Sun ◽  
Yangquan Chen ◽  
Wen Chen
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Diffusion Processes ◽  
Time Derivative ◽  
Equation Model ◽  
Differential Equation Model ◽  
New Model ◽  
Potential Applications ◽  
Fractional Differential ◽  
Derivative Order

This paper proposes a new type of fractional differential equation model, named time fractional differential equation model, in which noise term is included in the time derivative order. The new model is applied to anomalous relaxation and diffusion processes suffering noisy field. The analysis and numerical simulation results show that our model can well describes the feature of these processes. We also find that the scale parameter and the frequency of the noise play a crucial role in the behaviors of these systems. At the end, we recognize some potential applications of this new model.

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