Principles of mathematical modeling of combined effects in biology and medicine. Review of the literature

Using the combined action of different factors on biological objects with different levels of genome organization in biology and medicine is now widespread. Increased attention to this problem was paid due to publications on importance of synergistic interactions between agents leading to increase in the observed effect. New knowledge identified the need to consider the qualitative nature of the interaction, as well as to quantify the value of synergy. In this regard, a large number of studies including mathematical modeling of combined effects of ionizing radiation and different physical and chemical agents were published in the literature. The continuation of this work was mathematical modeling of interactions between different therapeutic agents. The application of mathematical models may be a significant contribution to the development of new ideas in utilization of combined chemical therapy by means of predicting the overall effect. The purpose of this review is to present a diversity of mathematical models of combined effects produced by various agents on biological objects and propose a modern vision of its application in biology and medicine for prediction of effects from combining different therapeutic agents.