M A SOHALY
Articles written in Pramana – Journal of Physics
Volume 95 All articles Published: 23 September 2021 Article ID 0157 Research Article
In this article, we applied the unified solver method to extract stochastic solutions of a new stochastic extension of nonlinear Schrödinger equation. This solver gives the closed formula in explicit form. The acquired stochastic solutions may be applicable for explaining some phenomena in many fields of applied sciences. The presented results illustrate that the proposed solver is efficient and adequate. Moreover, the constraint conditions are utilised to verify the existence of solutions. Chi-square statistical distribution is chosen to represent the dispersion random input. In order to illustrate the dynamical behaviour of random solutions, the expectation value and their variance are depicted graphically using suitable parameters.
Volume 96 All articles Published: 13 January 2022 Article ID 0022 Research Article
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$^d$$_0$ of the deterministic model and of the corresponding stochastic model are identified. Using appropriate Lyapunov functionals, we obtain sufficient conditions for the extinction of the disease by studying the dynamics of the disease-free equilibrium E$_0$. We show the regions of stability of E$_0$ and some computer simulations are carried out to present the effect of the stochastic environmental noise and the delay tactics. Sensitivity of R$^s$$_0$ with respect to the noise parameter σ and the delay $\tau$ is shown. Our study shows that the increase in the delay tactics and the noise help in the possible extinction, as needed.
Volume 97, 2023
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