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In recent years, mathematical modeling has played a key role in many life applications such as computer science, physics, chemistry, and genetics. Actually, in this paper, our focus is on the classifications and the importance of mathematical programming and its applications in health problems especially the Mathematical Modeling of COVID_19. According to the era of the Corona pandemic, it has been using mathematical equations to employ mathematical programming in epidemics and the mechanism of spreading in urban areas. The solution of the problem is presented in two directions; the first was by graphic representation and the other by using computational software via the Python language. [ABSTRACT FROM AUTHOR]

In this paper we consider a controlled dynamical system consisting of two objects in the presence of external perturbations. The dynamics of the first object (the main object of the system) and the second object (the auxiliary object of the system) are described respectively by linear and nonlinear discrete-time recurrent vector equations. In the system under consideration there are two levels of control: basic level (the level I) that is dominant level and auxiliary level (the level II) that is subordinate level. The quality of the control process on every level of the control system is estimated by corresponding convex terminal functional. Both the control levels have different informational and control connections defined in advance. In this paper we study the problem of optimization of guaranteed result for program control the final state of phase vectors of the objects in the presence of external perturbations. For this problem we propose a mathematical formalization of two-level hierarchical minimax program control the final state of the dynamical system in the presence of external perturbations and incomplete information. In this paper for solving of the investigated problem is proposed the algorithm that has a form of a recurrent procedure of solving a linear and a convex mathematical programming problems, and a finite optimization problems. [ABSTRACT FROM AUTHOR]

Nowadays, with the popularity of the computers, various industries and fields are widely applying computer information technology, which brings about huge demand for a variety of application software. In order to develop software meeting various needs with most economical cost and best quality, programmers must design efficient algorithms. A superior algorithm can not only soul up one thing, but also maximize the benefits and generate the smallest overhead. As one of the common algorithms, dynamic programming algorithms are used to solving problems with some sort of optimal properties. When solving problems with a large amount of sub-problems that needs repetitive calculations, the ordinary sub-recursive method requires to consume exponential time, and dynamic programming algorithm can reduce the time complexity of the algorithm to the polynomial level, according to which we can conclude that dynamic programming algorithm is a very efficient compared to other algorithms reducing the computational complexity and enriching the computational results. In this paper, we expound the concept, basic elements, properties, core, solving steps and difficulties of the dynamic programming algorithm besides, establish the dynamic programming model of the production planning problem [ABSTRACT FROM AUTHOR]

The developed method of iterative optimization of interplanetary missions with the low thrust, using sequence of movement specified mathematical models and design shape spacecraft, is realized. The new articular analytical decision describing planar movement of spacecraft with solar electric propulsion is described, allowing to construct initial approach in the iterative scheme of optimization. Developed a method of modelling and optimization of interplanetary missions ballistic schemes, based on a combination of Pontryagin's maximum principle formalism conditions of transversality and methods of the mathematical programming, allowing to consider restrictions characteristic for concrete interplanetary missions. Recommendations for choice design-ballistic parameters of the interplanetary missions spacecraft, received taking into account features nuclear and solar power plant for missions on delivery of a payload to orbits of Mars, expeditions the Earth-Mars-Earth are received. [ABSTRACT FROM AUTHOR]