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Asymptotic stability of solutions for a diffusive epidemic model

Bouaziz Khelifa, Douaifia Redouane, Abdelmalek Salem

Demonstratio Mathematica

2022

Vol. 55, nr 1

553--573

The aim of this paper is to study the existence and the asymptotic stability of solutions for an epidemiologically emerging reaction-diffusion model. We show that the model has two types of equilibrium points to resolve the proposed system for a fairly broad class of nonlinearity that describes the transmission of an infectious disease between individuals. The model is analyzed by using the basic reproductive number R0 . Finally, we present the numerical examples simulations that clarifies and confirms the results of the study throughout the paper.

Reaction-diffusion problems with Random parameters using the generalized stochastic finite difference method

Kamiński M.

Journal of Applied Computer Science

2011

Vol. 19, nr 2

31-45

The main idea here is to demonstrate the new stochastic discrete computational approach consisting of the generalized stochastic perturbation technique based on the Taylor expansions of the random variables and, at the same time, classical Finite Difference Method on the regular grids. As it is documented by the computational illustrations, it is possible to determine using this approach also higher probabilistic moments and to provide full hybrid analytical-discrete analysis for any random dispersion of input variables unlike in the second order second moment technique worked out before. A numerical algorithm is implemented here using the straightforward partial differentiation of the reaction-diffusion equation with respect to the random input quantity; all symbolic computations of probabilistic moments and characteristics are completed by the computer algebra system MAPLE.