Mohammed Mahyoub Ali Al-Shamiri

The World Health Organization (WHO) constantly reports outbreaks of dengue, mostly in different countries of tropical and subtropical regions. The most alarming effect of dengue is that there is no specific medical treatment for this sessional disease. Delaying the transmission of dengue is one of anticipation. So, in this continuation paper, first, we presented the previously missing dynamical analysis of the deterministic dengue system, including positivity, boundedness, and asymptotic behavior of system convergence around the consequent equilibrium states. Parameter sensitivity concerning the reproductive number is investigated and graphically explained. Derivation of the stochastic delayed dengue model by the non-parametric perturbation technique is presented and its global positivity is investigated. The proposed non-standard finite difference theoretical and continuous analysis is presented. First, the sensitivity of model parameters about the reproductive number is explained and simulated. Second, we discuss whether the numerical analysis of the previously discussed schemes for the stochastic dengue model also effectively functions for the stochastic delayed dengue mathematical model. Finally, the classical impact of delayed tactics on the stochastic delayed model and reproductive number is explained rigorously.

Stochastic delayed modeling (stochastic differential equations [SDEs] with delay parameters) has a significant nonpharmaceutical intervention to control transmission dynamics of infectious diseases, and its results are close to the reality of nature. According to the report of the World Health Organization (WHO), 296 million people are infected, and approximately 1.5 million people report positive tests for Hepatitis B each year. Hepatitis B is still a threat in developing and developed countries and appears in different variants globally. The present study is an extension of the deterministic hepatitis B model into a stochastic delayed model. The incorporation of stochasticity with delay in each compartment of the population like the S(t) susceptible population, P(t) acute infection, Q(t) chronic carriers' cases, R(t) immunization cases, and H(t) vaccinated class. The essential properties like positivity, boundedness, existence, uniqueness, equilibria (hepatitis‐free equilibrium [HFE] and hepatitis‐existing equilibrium [HEE]), reproduction number, sensitivity analysis, and stability result in the sense of local and second‐order stability result in the sense of global are studied rigorously before an extension of the model. The nonparametric perturbation and transition probabilities ways used to extend analysis. Also, the positivity, boundedness, extinction, and persistence of disease are studied rigorously. Due to the high complexity of nonlinear stochastic delay differential equations, computational methods are used to visualize the results with data from the model. Unfortunately, the existing methods (Euler–Maruyama, stochastic Euler, and stochastic Runge–Kutta) in the literature fail to restore the dynamical properties of the model and make a comparison with the newly proposed construction of nonstandard finite difference method in the sense of stochastic. In the proposed method, all dynamic properties of the model are restored with a free choice of time steps, and it is efficient. For convenience, a computational code of the nonstandard discrete model may be provided to the readers at their request.

According to the report of Statista, in 2023, the worldwide number of malware attacks reached 6.06 billion, an increase of 10 percent compared to the preceding year. In recent years, the highest number of malware attacks was detected in 2018, when 10.5 billion such attacks were reported across the globe. In the present study, to analyze the dynamics of viruses in the computer population, a delay tactics technique was used with the artificial decay parameters like different types of antivirus. The mathematical delayed model is designed with the whole computer population divided into subpopulations: susceptible, antidotal, exposed, infected, quarantined, and recovered. The fundamental properties of the newly developed model were studied rigorously like the positivity and boundedness of the results. Also, the two states discussed the computer population like computer virus–free equilibrium (virus control in computer populations) and computer virus–existing equilibrium (virus active to affect a computer population). Established concepts such as the Routh–Hurwitz criterion and Lyapunov function stabilities for both states of the model at the local and global levels under certain assumptions of reproduction number. The simulation results support the theoretical analysis of the model and the best presentation of results in each computer subpopulation. Also, these results visualize the gaining virus capacity and controlling virus with the effective use of delay tactics including or without antivirus software.

The present study investigated the dynamics of the nonlinear stochastic pine wilt epidemic model. An extension of the stochastic to deterministic model is presented. Equilibria, positivity, boundedness, extinction, and disease persistence were studied rigorously. Standard and nonstandard numerical techniques like Euler–Maruyama, stochastic Euler, stochastic Runge–Kutta, and stochastic nonstandard finite difference are presented for computational analysis. Furthermore, the nonstandard method is a dynamically consistent approximation of stochastic differential equations of the pine wilt epidemic model that is efficient, low cost, and independent of time‐step size. The comparison section with standard methods strengthens the nonstandard method and supports the theoretical results of the model.

A multigranulation roughness over dual universes establishes a unique viewpoint on the mixture of multigranulation data. Spherical fuzzy set is an extension of all existing theories such as fuzzy set, pythagorean fuzzy set, intuitionistic fuzzy set, and picture fuzzy set. This theory gives a more flexible structure for handling uncertainty and inaccuracy in decision‐making problems compared to all the extensions of fuzzy set. This paper introduces optimistic multigranulation roughness of a spherical fuzzy set based on two soft binary relations over dual universes. In this regard, we obtain two spherical fuzzy soft sets with respect to foresets and aftersets. A comprehensive study of the basic properties of this new approach has been studied in order to explore this concept. Then, by extending this idea, we present optimistic multigranulation roughness of a spherical fuzzy set over dual universes based on multiple soft binary relations. Moreover, a decision‐making algorithm depending on these approximations of spherical fuzzy sets is presented, and a practical example to choose a university professor is given. Two different panels of interviewers analyze the candidates based on different parameters by using the spherical fuzzy concept. This approach will be better and more flexible than other existing techniques.