scholarly journals Dynamic characterization of a stochastic SIR infectious disease model with dual perturbation

2021 ◽  
pp. 2150016
Author(s):  
Driss Kiouach ◽  
Yassine Sabbar
Keyword(s):  
Disease Transmission ◽  
Random Perturbation ◽  
Gaussian White Noise ◽  
Asymptotic Properties ◽  
Disease Model ◽  
Infectious Disease Model ◽  
Environmental Perturbations ◽  
Persistence In The Mean ◽  
Mean Ergodicity ◽  
Perturbed Model

Environmental perturbations are unavoidable in the propagation of infectious diseases. In this paper, we introduce the stochasticity into the susceptible–infected–recovered (SIR) model via the parameter perturbation method. The stochastic disturbances associated with the disease transmission coefficient and the mortality rate are presented with two perturbations: Gaussian white noise and Lévy jumps, respectively. This idea provides an overview of disease dynamics under different random perturbation scenarios. By using new techniques and methods, we study certain interesting asymptotic properties of our perturbed model, namely: persistence in the mean, ergodicity and extinction of the disease. For illustrative purposes, numerical examples are presented for checking the theoretical study.

DECISION MAKING IN MODELING THE DYNAMICS OF INFECTIOUS DISEASE TAKING INTO ACCOUNT DIFFUSION DISTURBANCES AND CONCENTRATED ACTIONS

2021 ◽  
Vol 3 ◽  
pp. 115-129
Author(s):  
Sergey Baranovsky ◽  
◽  
Andrey Bomba ◽  
Sergey Lyashko ◽  
◽  
...  
Keyword(s):  
Infectious Disease ◽  
Disease Model ◽  
Maximum Level ◽  
Viral Disease ◽  
The Body ◽  
Diverse Range ◽  
Infectious Disease Model ◽  
Short Period ◽  
Spatially Distributed ◽  
Perturbed Model

To study the patterns of response of the immune system to viruses detected in the body, a very diverse range of models has been developed. The simplest infectious disease model, which describes the most general mechanisms of immune protection, built on the assumption that the environment of the «organism» is homogeneous, in which all components of the process are instantly mixed by Marchuk is known. The infectious disease mathematical model by Marchuk for generalization of diffusion perturbations and various concentrated influences is generalized. The corresponding singularly perturbed model problem with delay is reduced to a sequence of problems without delay, for which the corresponding asymptotic developments of solutions are obtained. The results of numerical experiments, which illustrate the influence of spatially distributed diffusion «redistributions» on the nature of the viral disease in the presence of concentrated sources of antigens and donor antibodies are presented. A model decrease in the maximum level of antigens in the infection epicenter due to their diffusion «erosion» in the process of infectious disease development has been demonstrated. It is emphasized that even if the initial concentration or intensity of the pulsed viral source in a certain part of the infection will exceed some critical value (immunological barrier) due to diffusion «redistribution» for a short period of time, the supercritical concentration of viral agents may decrease to lower than the critical level and further neutralization of antigens can be provided by the available level of antibodies and a more economical procedure of injection solution with donor antibodies. That is, within this model, the «severity» of the viral disease in such cases can be reduced more rationally, at lower cost.

scholarly journals Prediction of Coronavirus Disease (covid-19) Evolution in USA with the Model Based on the Eyring’s Rate Process Theory and Free Volume Concept

2020 ◽  
Author(s):  
Tian Hao
Keyword(s):  
Infectious Disease ◽  
Free Volume ◽  
Disease Transmission ◽  
Disease Model ◽  
Human Movement ◽  
Process Theory ◽  
Rate Process ◽  
Infectious Disease Model ◽  
Reaction Rate Constants ◽  
Rate Process Theory

AbstractA modification arguing that the human movement energy may change with time is made on our previous infectious disease model, in which infectious disease transmission is considered as a sequential chemical reaction and reaction rate constants obey the Eyring’s rate process theory and free volume concept. The modified model is employed to fit current covid-19 outbreak data in USA and to make predictions on the numbers of the infected, the removed and the death in the foreseeable future. Excellent fitting curves and regression quality are obtained, indicating that the model is working and the predictions may be close to reality. Our work could provide some ideas on what we may expect in the future and how we can prepare accordingly for this difficult period.

scholarly journals DNA Epidemic Model Construction and Dynamics Optimization

2020 ◽  
Vol 14 (3) ◽  
pp. 97-117
Author(s):  
Yinglian Zhou
Keyword(s):  
Infectious Disease ◽  
Disease Transmission ◽  
Optimization Problems ◽  
Disease Model ◽  
Sir Model ◽  
Test Results ◽  
Infectious Disease Model ◽  
Exchange Information ◽  
Complex Optimization ◽  
Dna Algorithm

In order to solve some complex optimization problems, the SIR-DNA algorithm was constructed based on the DNA-based SIR (susceptible-infectious-recovered) infectious disease model. Since infectious diseases attack a very small part of the individual's genes, the number of variables per treatment is small; thus, the natural dimensionality reduction of the algorithm is achieved. Based on the DNA-SIR infectious disease model, different infections can be distinguished in the pathogenesis of viruses. The mechanisms of disease transmission are described by the SIR model, and these are used to construct operators such as SS, SI, II, IR, RR, and RS, so that individuals can naturally exchange information naturally through disease transmission. The test results show that the algorithm has the characteristics of strong search ability and has a high convergence speed for solving complex optimization problems.

scholarly journals Global Dynamics of SIRS Model with No Full Immunity on Semidirected Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Jiawei Huo ◽  
Yimin Li ◽  
Jing Hua
Keyword(s):  
Disease Transmission ◽  
Disease Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Scale Free ◽  
Infectious Disease Model ◽  
Sirs Model ◽  
Self Protection ◽  
Full Immunity

In this paper, an epidemic model with no full immunity is analyzed on semidirected networks. Directed networks led into previous scale-free networks, and we consider that some infectious diseases do not have full immunity. So we use strong self-protection instead of immunity and establish a semidirected network infectious disease model without full immunity. The basic reproduction number R0 is calculated. If R0<1, the disease-free equilibrium E0 is locally and globally asymptotically stable. And the endemic equilibrium E∗ is globally asymptotically stable in some condition. A large number of simulation results in this paper verify the correctness of the above conclusions and provide a solution for controlling disease transmission in the future.

scholarly journals Obesity as an "infectious" disease

2021 ◽  
Vol 11 (9) ◽  
pp. 534-537
Author(s):  
Daria Żuraw ◽  
Paulina Oleksa ◽  
Mateusz Sobczyk
Keyword(s):  
Infectious Disease ◽  
Disease Model ◽  
Living Environment ◽  
Social Contagion ◽  
Social Discrimination ◽  
Obese People ◽  
Obesity Epidemic ◽  
Global Epidemic ◽  
Infectious Disease Model ◽  
The One

Introduction: Obesity has been recognized as a global epidemic by the WHO, followed by a wealth of empirical evidence supporting its contagiousness. However, the dynamics of the spread of obesity between individuals are rarely studied.  A distinguishing feature of the obesity epidemic is that it is driven by a process of social contagion that cannot be perfectly described by the infectious disease model. There is also social discrimination in the obesity epidemic. Social discrimination against obese people plays quite different roles in two cases: on the one hand, when obesity cannot be eliminated, social discrimination can reduce the number of obese people; on the other hand, when obesity is eradicable, social discrimination can cause it to explode.(1)   Materiał and methods: A literature analysis on obesity epidemic was carried out within the Pubmed, Google scholar and Research Gate platform. The following keywords were used in serach: obesity, epidemy, children, body max index.    Purpose of the work: The aim of the following analysis is to present an obesity as an infectious disease. The steadily increasing percentage of obese people, including children, shows that there is an obesity epidemic. This is the phenomenon of social contagion, which partially explains the concept of homophily, which involves the grouping of people with similar characteristics. Potential explanations are also provided by sharing a living environment with similar access to certain foods and similar opportunities for physical activity, which defines the occurrence of analogous health habits

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