Моделирование влияния рекомендаций на приток пациентов в сеть клиник

Abstract

The work deals with mathematical modeling of referral activities of the consumers who have received experience of physical therapy rehabilitation (PTR). The relevance of the work is determined by the importance of the development of rehabilitation activities and the creation of a network of treatment centers of walking distance. A mathematical model of the influence of referral feedback on the flows of customers entering treatment has been developed, as well as the estimates of the growth in the number of patients have been carried out. The main groups of patients influencing the number of patients undergoing treatment (Y) are: those continuing treatment (A), those recovered (B), those dissatisfied with treatment (C) and those choosing another method of restoring health (D). The main factor characterizing the flow of patients to the clinic is the “recommendation parameter” – R, which depends on eight coefficients characterizing the recommendation process. The differential equation of the flow of patients to the clinic, depending on time T, is dY/dT = H – YR, where H is the flow of patients under the influence of promotion. The analytical solution of this equation is expressed by the formula Y = HR(1 – Exp(-T/R)). The maximum number of patients is directly proportional to the promotion effect (H) and the recommendation parameter (R). The main factors affecting the value of the recommendation parameter are the proportion of patients who continue treatment (a) and the recommendation influence coefficient of these patients KA. As the number of clinic customers grows, promotion activity can be reduced without a significant drop in customer flow. The results can be used to intensify recommendation activity in the service sector.