In the paper, differential quadrature method (DQM) is used to find numerical solutions of reaction-diffusion equations with different boundary conditions. The DQM-method changes the reaction- diffusion equation (ordinary differential equation) into a system of algebraic equations. The obtained system is solved using built-in procedures of Maple®(Computer Algebra System-type program). Calculations were performed with Maple®program. The test problems include reaction-diffusion equation applied in heterogeneous catalysis. The method can be employed even in relatively hard tasks (e.g. ill-conditioned, free boundary problems).

We build a mathematical game model of pandemic transmission, including vaccinations of population and budget costs of different acting to eliminate pandemic. We assume the interactions among different groups: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, defining a system of ordinary differential equations, which describes compartment model of disease and costs of the treatment. The goal of the game is to describe the development disease under different types of treatment, but including costs of them and social restrictions, during the shortest time period. To this effect we construct a dual dynamic programming method to describe open-loop Nash equilibrium for treatment, a group of people having antibodies and budget costs. Next, we calculate numerically an approximate open-loop Nash equilibrium.