Stochastic SIS Research Articles

Intelligent Adaptive Networks for Chaos Analysis in Stochastic SIS Differential Epidemic Model with the Impact of Unpredictable Environmental Factors

In this study, an intelligent computing framework is presented to explore the influence of unpredictable environmental factors on the spread of infections. A stochastic non-linear SIS epidemic model (SISEM) is examined that incorporates a non-linear incidence rate, and impact of random fluctuations on the disease transmission. The knacks of artificial neural networks Levenberg–Marquardt (ANNLMA) technique are exploited to illustrate the behavioral complexities of stochastic non-linear SISEM, which explores the dynamics of disease transmission in a stochastic environment and provides insights into the interactions between susceptible and infectious populations. The Milstein approach of order 1 generates a dataset for the proposed ANNLMA technique by varying integrated parameters, such as the rates of recovery, death, disease transmission, noise standard deviation and the entire population, for various SISEM scenarios. The referenced dataset is randomly divided into test, validation and train sets for the weight learning of the proposed ANNLMA. The viability of the ANNLMA is measured using intensive simulation-based investigations through analysis of mean squared errors, histograms, regression and autocorrelation studies. The investigations highlighted that the ANNLMA results closely match the reference results, illustrating convergence within the 10[Formula: see text] to 10[Formula: see text] range, indicating the validity of the proposed methodology.

Fokker–Planck equation and Feynman–Kac formula for multidimensional stochastic dynamical systems with Lévy noises and time-dependent coefficients

The aim of this paper is to establish a version of the Feynman–Kac formula for the time-dependent multidimensional nonlocal Fokker–Planck equation corresponding to a class of time-dependent stochastic differential equations driven by multiplicative symmetric (or asymmetric) α-stable Lévy noise. First the forward nonlocal Fokker–Planck equation is derived by the adjoint operator method, overcoming the challenges posed by time-dependent multidimensional nonlinear symmetric α-stable Lévy noise. Subsequently, the Feynman–Kac formula for the forward multidimensional time-dependent nonlocal Fokker–Planck equation is established by applying techniques for the backward nonlocal Fokker–Planck equations, which is associated with the backward stochastic differential equation driven by the multiplicative symmetric α-stable Lévy noise. Notably, in the case of asymmetric α-stable Lévy noise case, the presence of the characteristic function in the nonlocal operator adds complexity to the analysis. Using the Feynman–Kac formula, it is demonstrated that the solution of the forward nonlocal Fokker–Planck equation can be readily simulated through Monte Carlo approximation, especially in scenarios involving long-time simulation settings with large steps. These concepts are illustrated with intriguing examples, and the dynamic evolution of the probability density function corresponding to the stochastic SIS model and the stochastic model for the MeKS network (reflecting the interactions among the MecA complex, ComK and ComS) are investigated over an extended period.

ROLE OF INTERVENTION STRATEGIES AND PSYCHOLOGICAL EFFECT ON THE CONTROL OF INFECTIOUS DISEASES IN THE RANDOM ENVIRONMENT

Infectious disease outbreaks have caused significant losses to populations worldwide in terms of morbidity, social and economic costs. This has prompted governments to seek suitable intervention policies to suppress the outbreaks. This paper aims to explore the intrinsic impact of intervention strategies and the psychological behavior of people on the spread of infectious diseases. Employing the finite state Markov chain, we formulate a new stochastic SIS epidemic model under regime switching by using the Beddington–DeAngelis transmission function, in the presence of some governmental control measures. The study of the model is centered on three different scenarios in terms of varying two control parameters. We analyze the deterministic system for the global dynamics in terms of basic reproductive number. Some new threshold parameters are defined to discuss the extinction and the persistence of the disease in the stochastic setting. Numerical assessments were undertaken to validate theoretical findings for the deterministic and stochastic systems. Our findings strongly suggest that heightened awareness among susceptible individuals contributes significantly to the eradication of infection and fosters a stable epidemiological situation. As levels of public awareness increase, particularly within the susceptible population, a discernible trend toward the eradication of the infection emerges, ultimately ensuring sustained stability within the epidemiological landscape.

Large population asymptotics for a multitype stochastic SIS epidemic model in randomly switching environment

Large population asymptotics for a multitype stochastic SIS epidemic model in randomly switching environment

Dynamical Behaviors of Stochastic SIS Epidemic Model with Ornstein–Uhlenbeck Process

Controlling infectious diseases has become an increasingly complex issue, and vaccination has become a common preventive measure to reduce infection rates. It has been thought that vaccination protects the population. However, there is no fully effective vaccine. This is based on the fact that it has long been assumed that the immune system produces corresponding antibodies after vaccination, but usually does not achieve the level of complete protection for undergoing environmental fluctuations. In this paper, we investigate a stochastic SIS epidemic model with incomplete inoculation, which is perturbed by the Ornstein–Uhlenbeck process and Brownian motion. We determine the existence of a unique global solution for the stochastic SIS epidemic model and derive control conditions for the extinction. By constructing two suitable Lyapunov functions and using the ergodicity of the Ornstein–Uhlenbeck process, we establish sufficient conditions for the existence of stationary distribution, which means the disease will prevail. Furthermore, we obtain the exact expression of the probability density function near the pseudo-equilibrium point of the stochastic model while addressing the four-dimensional Fokker–Planck equation under the same conditions. Finally, we conduct several numerical simulations to validate the theoretical results.

A double stochastic SIS network epidemic model with nonlinear contact rate and limited medical resources

A double stochastic SIS network epidemic model with nonlinear contact rate and limited medical resources

Certain aspects of the SIS stochastic epidemic model

The SIS model is a fundamental tool in epidemiology for understanding the spread of infectious diseases. This article focuses on the stochastic SIS model, introducing randomness through the disease transmission parameter. The study investigates the behavior of the model, revealing the conditions for the recurrence or extinction of the disease. In particular, it addresses the calculation of the conditional expected time for the disease to exceed a certain threshold, using both Laplace transforms and numerical techniques for its specific application. Real-world phenomena are discussed, and a method for determining the most suitable stochastic parameter is proposed, with examples such as gonorrhea and pneumococcus.

Novel intelligent predictive networks for analysis of chaos in stochastic differential SIS epidemic model with vaccination impact

In this paper, stochastic predictive computing networks are exploited to investigate the dynamics of the SIS with vaccination impact based epidemic model (SISV-EM) represented by nonlinear systems of stochastic differential equations (SDEs) by exploitation of artificial neural networks (ANNs) with the backpropagated Levenberg-Marquardt technique (BLMT) i.e., (ANNs-BLMT) to approximate the solution behavior. The stochastic nonlinear SISV-EM is governed with three classes: susceptible, infectious, and vaccinated populations. The referenced or target datasets for ANNs-BLMT are constructed by employing Euler-Maruyama (EM) scheme for solving stochastic differential systems in case of sufficiently various nonlinear SISV-EM scenarios by varying the percentage of vaccination for newly born, the coefficient of transmission, the natural mortality rates, the infectious rates of recovery, the rate at which vaccinated people lose their immunity, the rate of death caused by disease, the proportion of vaccinated against susceptible and the white noise in the environment. Based on arbitrary training, testing, and validation samples from the referenced dataset, the ANNs-BLMT provides an approximate solution for the stochastic nonlinear SISV-EM, with significant correlations to the referenced results. Exhaustive simulation-based results using error histograms, mean square errors, and regression analyses further demonstrate that the proposed ANNs-BLMT is efficient, consistent, and accurate for solving SISV-EM.

Stochastic modeling of SIS epidemics with logarithmic Ornstein–Uhlenbeck process and generalized nonlinear incidence

In this paper, we investigate a stochastic SIS epidemic model with logarithmic Ornstein–Uhlenbeck process and generalized nonlinear incidence. Our study focuses on the construction of stochastic Lyapunov functions to establish the threshold condition for the extinction and the existence of the stationary distribution of the stochastic system. We also derive the exact expression of the density function around the quasi-endemic equilibrium, which provides valuable insight into the transmission and progression of the disease within a population. Our findings demonstrate the importance of considering the impact of stochasticity on the spread of epidemics, particularly in the presence of complex incidence mechanisms and stochastic environmental factors. Additionally, the stochastic threshold reveals that ordinary differential equation models and white noise models underestimate the severity of disease outbreaks, while our proposed the stochastic epidemic model with logarithmic Ornstein–Uhlenbeck process accurately captures real-world scenarios.

Examining the Relationship Between Infection Power Rate and the Critical Threshold in Stochastic SIS Epidemic Modeling

The stochastic SIS epidemic model is well-known for its critical threshold Rs, indicating the transition between disease eradication (Rs < 1) and epidemic outbreaks (Rs > 1). However, the scenario where Rs = 1 has been uncertain. We present a definitive resolution to this pivotal issue. Additionally, we introduce advancements in analyzing the disease-free state of equilibrium when Rs < 1 to deepen our understanding of the system dynamics. To validate our theoretical developments and provide visual evidence, extensive computer simulations are conducted, enhancing the comprehensiveness and applicability of our findings to the broader field of epidemiology and infectious disease modeling. The implications of our results extend to public health policies and interventions aimed at effectively managing and controlling infectious diseases in different communities where Rs hovers around the critical value.

Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model

Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model

On the extinction of stochastic Susceptible-Infected-Susceptible epidemic with distributed delays

In this paper, we study a stochastic SIS epidemic model with distributed delays. The positiveness of the solutions is established. We obtain sufficient conditions for the extinction of the disease through the study of stochastic stability of the disease-free equilibrium and stability of the same equilibrium in the mean. Compared to many works on the deterministic and stochastic SIS models and their stability, the distributed delays involved in the model offer new conditions with much more boundedness on the rate of losing immunity. The disease is extinct for small and large enough values of the intensity of noise and regardless of the initial history functions and the magnitude of the basic reproductive number R0.

A stochastic SIS epidemic infectious diseases model with double stochastic perturbations

In this paper, a stochastic SIS epidemic infectious diseases model with double stochastic perturbations is proposed. First, the existence and uniqueness of the positive global solution of the model are proved. Second, the controlling conditions for the extinction and persistence of the disease are obtained. Besides, the effects of the intensity of volatility [Formula: see text] and the speed of reversion [Formula: see text] on the dynamical behaviors of the model are discussed. Finally, some numerical examples are given to support the theoretical results. The results show that if the basic reproduction number [Formula: see text], the disease will be extinct, that is to say that we can control the threshold [Formula: see text] to suppress the disease outbreak.

A stochastic simplicial SIS model for complex networks

We propose a stochastic epidemiological model for simplicial complex networks by means of a stochastic differential equation (SDE) that extends the mean field approach of the simplicial social contagion model. We show that, under appropriate conditions, if the stochastic basic reproductive number is smaller than one, then the disease dies out with probability one; otherwise the solution of the SDE oscillates infinitely often around a point which can be explicitly computed. We perform numerical experiments which illustrate the theoretical results. In addition, we carry out simulations on a real simplicial network and on a synthetic network, which show good agreement with the theoretical and numerical predictions of the SDE.

A Sufficient Condition for Extinction and Stability of a Stochastic SIS Model With Random Perturbation

The system dynamics of the randomly perturbed SIS depend on a certain threshold RS. If RS < 1, the disease is removed from our community, whereas an epidemic will occur if RS > 1. However, what happens when RS = 1? In this paper, we give a solution to this problem. Furthermore, we make some improvements to the free disease equilibrium state E0 when RS < 1. Last, we give some computational simulations to explain our results.

A stochastic delayed SIS epidemic model with Holling type II incidence rate

In this article, a stochastic SIS epidemic model with constant time delay and Holling type II incidence rate is investigated. We firstly show the existence, uniqueness, and moment boundedness of the global positive solution. Then we extend the initial value space to a complete nonnegative continuous function space and obtain the existence of invariant measures for this system. Furthermore, the analysis of the asymptotic behavior around the disease-free equilibrium is given. To demonstrate, some numerical examples are provided to illustrate our results.

Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model

Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model

Using Stochastic SIS Epidemic Model with Markovian Environment for Infectious Diseases

There are various types of stochastic epidemic models that can be formulated to deal with different types of diseases. In this project (SIS) epidemic model Susceptible - Infected- Susceptible will be considered relating to the Continuous Time Markov chains process. Each type of the epidemic models studies the disease according to its status. In particular, the SIS epidemic model regards infectious diseases. The Maple code is provided in this project, which is created to produce and predict the number of infected individuals and the disease prevalence at a fixed time.

Optimal consumption and portfolio choices in the stochastic SIS model

Motivated by the stochastic SIS model, this paper aims to incorporate the stochastic transmission shock (e.g., COVID−19) into the standard portfolio theory, and explores the optimal rules with respect to infections. The impact of COVID−19 is decomposed into two dimensions such as infectivity (denoted by R0) and infection rate (measured by I). The results indicate that infectivity mainly affects consumption, whereas the investment rule is merely governed by infection rate. Moreover, we find that higher infections lead to less sensitivity and smoother consumption compared with normal times. However, the sensitivity and volatility of investment with respect to infections present a U-shape and hump-shape, respectively. Notably, we shed new lights on the effect of transmission uncertainty and risk-aversion with pandemic shock. The innovative attempt of this paper not only enriches the research of epidemiology in the field of economics, but also provides a paradigm for studying investor’s behavior under the normalization of epidemic situations.

Stochastic dynamics of an SIS epidemiological model with media coverage

In this paper, we establish a stochastic SIS epidemic model with general transmission function and media coverage, and prove that two thresholds R1s and R2s (R2s<R1s) can be used to govern the stochastic dynamics of the stochastic SIS model. If R1s<1, the disease will die out with probability one and the distribution of the susceptible converges weakly to a boundary distribution; while if R2s>1, the disease is persistent almost surely and there exists a unique stationary distribution. Furthermore, we study the disease dynamics when R2s<1<R1s numerically, and find that the disease dynamics in this range is rich and complex, i.e., the disease may persist or extinct. Epidemiologically, we find that the smaller the intensity of random disturbance, the smaller the oscillation amplitude of the solution, and as the intensities of random disturbance increase, the mean of the infectious decreases and the distribution of them becomes more and more right-skewed, which provide a theoretical basis for disease control.