Mathematical exploration of a diffusive infection's dynamics and simulation.

In this work, we construct Lyapunov functionals to analyze the global stability of the equilibria in reaction-diffusion systems arising in biological models. We employ Lyapunov functionals originally constructed for associated ordinary differential equation (ODE) models and extend them to partial differential equation (PDE) systems involving spatial diffusion. We analyze disease-free and endemic equilibrium stability in terms of the basic reproduction number [Formula: see text] a threshold parameter.

Investigating the stochastic higher dimensional nonlinear Schrodinger equation to telecommunication engineering.

In this paper, we examine numerous soliton solutions of the nonlinear (3+1)-dimensional stochastic Schrödinger equation which is indispensable for describing wave propagation in noisy or random conditions, and catches the interaction between nonlinearity and stochasticity. The proposed model is applicable in various fields, namely optics, fluid dynamics, Bose-Einstein condensates, and plasma physics. It is fundamental to explain processes like phase transitions, noise-induced stability, and solitonal resilience.

Clinical and immunological parameters in patients infected with Cutaneous Leishmaniasis: Case control study- investigation of fractal fractional mathematical model in Lebesgue space.

Cutaneous Leishmaniasis (CL) is a skin disease that causes plaques, ulcers, and nodules on various body parts. The first aim of this study is to investigate the effect of CL on hematological and immunological markers. A total of 180 individuals (80 cases and 100 controls) examined.

Numerical Solutions of Variable Coefficient Higher-Order Partial Differential Equations Arising in Beam Models.

In this work, an efficient and robust numerical scheme is proposed to solve the variable coefficients' fourth-order partial differential equations (FOPDEs) that arise in Euler-Bernoulli beam models. When partial differential equations (PDEs) are of higher order and invoke variable coefficients, then the numerical solution is quite a tedious and challenging problem, which is our main concern in this paper. The current scheme is hybrid in nature in which the second-order finite difference is used for temporal discretization, while spatial derivatives and solutions are approximated via the Haar wavelet.

Future implications of COVID-19 through Mathematical modeling.

COVID-19 is a pandemic respiratory illness. The disease spreads from human to human and is caused by a novel coronavirus SARS-CoV-2. In this study, we formulate a mathematical model of COVID-19 and discuss the disease free state and endemic equilibrium of the model.

Stability analysis and simulation of the novel Corornavirus mathematical model via the Caputo fractional-order derivative: A case study of Algeria.

The novel coronavirus infectious disease (or COVID-19) almost spread widely around the world and causes a huge panic in the human population. To explore the complex dynamics of this novel infection, several mathematical epidemic models have been adopted and simulated using the statistical data of COVID-19 in various regions. In this paper, we present a new nonlinear fractional order model in the Caputo sense to analyze and simulate the dynamics of this viral disease with a case study of Algeria.

Modeling the transmission dynamics of middle eastern respiratory syndrome coronavirus with the impact of media coverage.

Middle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation.

Modeling the pandemic trend of 2019 Coronavirus with optimal control analysis.

In this work, we propose a mathematical model to analyze the outbreak of the Coronavirus disease (COVID-19). The proposed model portrays the multiple transmission pathways in the infection dynamics and stresses the role of the environmental reservoir in the transmission of the disease. The basic reproduction number is calculated from the model to assess the transmissibility of the COVID-19.

Analytical Solutions of a Modified Predator-Prey Model through a New Ecological Interaction.

The predator-prey model is a common tool that researchers develop continuously to predict the dynamics of the animal population within a certain phenomenon. Due to the sexual interaction of the predator in the mating period, the males and females feed together on one or more preys. This scenario describes the ecological interaction between two predators and one prey.