Mathematical modeling of viral hepatitis B

Abstract

Studies of spatiotemporal models of viral infections have become an indispensable tool for biological researchers, as they can improve the understanding of the dynamics of the virus inside the target, in particular the population of viral particles in interaction with other populations, the mathematical models of which are described by the corresponding boundary value problems of mathematical physics for partial differential equations. Existing publications on spatiotemporal models of hepatitis B populations are limited to the formulation of mathematical models. Therefore, our goal is to develop numerical-analytical methods for the study of nonlinear spatiotemporal models with the subsequent use of these solutions for the synthesis of optimal control of doses of picaric drugs, with the aim of reducing (or completely neutralizing) the impact of viruses on the target organ. The application of the numerical-analytic iterative method, based on the use of the method of integral transformations, made it possible to obtain approximate solutions of the corresponding boundary value problems for systems of nonlinear partial differential equations obtained in quadratures, which makes it possible to simulate the synthesis of optimal control in real time (in contrast to the possible use of the corresponding difference schemes for this purpose