A mathematical model for the customer dynamics based on marketing policy

TL;DR

This paper introduces a compartmental mathematical model to analyze how marketing strategies influence the evolution of regular and referral customers within a corporation, considering social network effects.

Contribution

It develops a novel compartmental model incorporating marketing policies and social network effects to study customer dynamics.

Findings

Model predicts long-term customer composition under different marketing strategies.

Simulation results illustrate the impact of marketing policies on customer growth.

The model's applicability is discussed through various scenarios.

Abstract

We consider a compartmental model to study the evolution of the number of regular customers and referral customers in some corporation. Transitions between compartments are modeled by parameters depending on the social network and the marketing policy of the corporation. We obtain some results on the asymptotic number of regular customers and referral customers in several particular scenarios. Additionally we present some simulation that illustrates the behavior of the model and discuss its applicability.