Optimization of the force exerted by the synergistic treatment-immune response interaction Optimización de la fuerza ejercida por la interacción sinérgica tratamiento-respuesta inmunitaria

Abstract

In physics, synergy is an action that involves the coordination of two or more causes or parts, whose effects will be greater than the sum of the individual effects. Measuring the synergistic strength of the treatment and the immune response working together is of vital importance to control physicochemical parameters in bacterial infections. In this sense, in this article we focus on analyzing the impact of synergy through an optimal control problem. To formulate and solve the problem we use conservation laws that characterize the main properties of the physical phenomenon. Specifically, we use the Pontryagin Minimum Principle to minimize a performance functional that measures the strength of the synergy between treatment and immune response. The numerical results suggest that the forces synergies must be proportional to each other to control bacterial spread.