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In this study, we investigate the impact of inherent randomness on fire spread rates, with a particular focus on the stochastic parameter ε, representing the ratio of effective to actual fuel bulk density. By employing various probability distributions, such as the beta random distribution model ε, we explore the complex interplay between wind and slope factors in determining fire behavior. Our 3D visualizations and density plots illuminate the multidimensional nature of fire spread, emphasizing the significant role of stochastic variability in enhancing the accuracy of fire behavior models. This approach not only deepens our theoretical understanding but also provides valuable insights for improving fire management strategies. [ABSTRACT FROM AUTHOR]

Through the application of mathematical epidemiology principles, the formulation of the soft drugs model is established, and the complete dynamics of this deterministic model are contingent upon the crucial parameter called the basic reproduction number, denoted as R 0 d . The stochastic soft drug epidemic models are developed by considering the parametric and non-parametric stochastic perturbation techniques. Dynamics of the two different stochastic models are determined using the analog stochastic thresholds R 0 s 1 , R 0 s 2 , respectively. Introducing suitable Lyapunov functionals enables us to establish sufficient axioms for the extinction and permanence of soft drug users in both deterministic and stochastic models. Moreover, the sensitivity of the deterministic and stochastic thresholds to some important parameters involved in the models is illustrated. For the verification of our theoretical results, we develop some numerical simulations using the Euler–Maruyama scheme. [ABSTRACT FROM AUTHOR]

In this paper, an epidemic SI model with n -infectious stages is studied. Lyapunov functions are used to conduct the global stability analysis for equilibrium points. The n -basic reproduction ratios R 1 , R 2 , ..., R n are computed, and the basic reproduction number ( R 0 ) is the max value between this ratios is obtained. For, j = 1 , 2 ,... , n when R j is less than one, all strains die out, and if it is greater than one, then persists. The disease-free and endemic equilibrium points are found, and we studied the global stability for them by using the direct Lyapunov functions. The Maple program is used for carrying a numerical simulations to support the analytically results. [ABSTRACT FROM AUTHOR]

This paper delves into the investigation of the COVID-19 dynamics within a host using the Target-Latent-Infected-Virus (TLIV) model, presenting a fresh approach compared to previous studies. Our model introduces a latent class and explores sensitivity analysis, aspects that have received limited attention in prior research. A significant contribution of this study is the analysis of both local and global stability of equilibrium states, subject to specific sufficient conditions based on the basic reproduction number R 0 . By examining these stability properties, we aim to gain insights into the factors underlying variations observed in the findings of different studies. Additionally, we identify the death rate of infected cells as the parameter most susceptible to influence in our model. To minimize its impact and facilitate recovery, it is crucial to implement appropriate medical therapies and consume immune-boosting foods. Some computer simulations are carried out to strengthen the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence, the boundedness, the asymptotic behavior, and the oscillatory behavior of the positive solutions of the fuzzy difference equation where , is a sequence of positive fuzzy numbers, , , and the initial conditions , , are positive fuzzy numbers, and is a positive integer. [ABSTRACT FROM AUTHOR]

A discrete-time predator–prey model is investigated in this paper. In considered model, the population is assumed to follow the model suggested by Ricker 1954. Existence and stability of equilibria are studied. Numerical simulations reveal that, depending on the parameters, the system has complicated and rich dynamics and can exhibit complex patterns. Also the bifurcation diagrams are presented. [ABSTRACT FROM AUTHOR]

In this paper, a new mathematical model that describes the dynamics of the within-host COVID-19 epidemic is formulated. We show the stochastic dynamics of Target-Latent-Infected-Virus free within the human body with discrete delay and noise. Positivity and uniqueness of the solutions are established. Our study shows the extinction and persistence of the disease inside the human body through the stability analysis of the disease-free equilibrium E 0 and the endemic equilibrium E ∗ , respectively. Moreover, we show the impact of delay tactics and noise on the extinction of the disease. The most interesting result is even if the deterministic system is inevitably pandemic at a specific point, extinction will become possible in the stochastic version of our model. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic delayed HIV/AIDS model involving humans with immunity is formulated. We study the dynamics of the mathematical model of HIV/AIDS epidemic with discrete and distributed delays. The basic reproduction number R 0 d of the deterministic model and R 0 s of the corresponding stochastic model are identified. Using appropriate Lyapunov functionals, we obtain sufficient conditions for the extinction of the disease by studying the dynamics of the disease-free equilibrium E 0 . We show the regions of stability of E 0 and some computer simulations are carried out to present the effect of the stochastic environmental noise and the delay tactics. Sensitivity of R 0 s with respect to the noise parameter σ and the delay τ is shown. Our study shows that the increase in the delay tactics and the noise help in the possible extinction, as needed. [ABSTRACT FROM AUTHOR]

This manuscript is involved in the study of stability of the solutions of functional differential equations (FDEs) with random coefficients and/or stochastic terms. We focus on the study of different types of stability of random/stochastic functional systems, specifically, stochastic delay differential equations (SDDEs). Introducing appropriate Lyapunov functionals enables us to investigate the necessary conditions for stochastic stability, asymptotic stochastic stability, asymptotic mean square stability, mean square exponential stability, global exponential mean square stability, and practical uniform exponential stability. Some examples with numerical simulations are presented to strengthen the theoretical results. Using our theoretical study, important aspects of epidemiological and ecological mathematical models can be revealed. In ecology, the dynamics of Nicholson's blowflies equation is studied. Conditions of stochastic stability and stochastic global exponential stability of the equilibrium point at which the blowflies become extinct are investigated. In finance, the dynamics of the Black–Scholes market model driven by a Brownian motion with random variable coefficients and time delay is also studied. [ABSTRACT FROM AUTHOR]

Phase change materials (PCMs) such as paraffin wax are used to store solar energy in the form of latent heat of melting, which can be used later when no solar radiation is available. However, paraffin wax has a low thermal conductivity, i.e., 0.25W/mK, which lowers the rate of heat transfer from the wax to the pipes of water heaters, especially when it solidifies over the pipes. An experimental setup was developed to investigate the influence of (1) finned pipes and (2) metallic strips on the performance of solar water heaters that contains a heat storage material, i.e., paraffin wax. It has been found that the presence of fins and metallic strips inside the wax is acting as channels of heat transfer across the wax, such that the heat transfer process continues even if the wax solidifies over the heat exchange pipes. Also, adding fins and metallic strips has enhanced the temperature homogeneity in the molten wax. The amount of heat energy released by the wax to the flowing water has increased by 47% in case of using finned water pipes than unfinned pipes, and by 304% in case of using copper strips. It can be concluded from the performed experiments that adding fins or metallic strips to solar water heaters that contain paraffin wax improves the heating capability of the water heater. [ABSTRACT FROM AUTHOR]

We investigate some qualitative behavior of the solutions of the difference equation xn+1 = axn -bxn/(cxn -dxn-1), n = 0, 1, … , where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants. [ABSTRACT FROM AUTHOR]

We investigate some qualitative behavior of the solutions of the difference equation xn+1 = axn -bxn/(cxn -dxn-1), n = 0, 1, … , where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants. [ABSTRACT FROM AUTHOR]

We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics behavior of the mathematical model of Human Immunodeficiency Virus (HIV) influenced by stochastic perturbations. This paper is involved in exploring the disease-free equilibrium’s stochastic global exponential stability with a basic reproductive number R 0 < 1 . Necessary and sufficient conditions for stochastic global exponential stability of the disease-free equilibrium E 0 of the nonlinear HIV stochastic system are derived. This can be accomplished by the exponential analysis of the global mean square stability of trivial equilibrium of the corresponding linear system. Finally, we provide areas of stability of E 0 and numerical simulations to confirm the analytical results by using the fundamental Euler–Maruyama (EM) algorithm. [ABSTRACT FROM AUTHOR]