A competitive infectious transmission model

Abstract

Compartmental disease transmission models are widely used to model state transmission in infectious diseases, using differential equations to model the change in the number of units in different states over time, and recently has produced significant practical implications in many downstream fields. However, inspired by the transmission of rumors in social media, we note that the previous compartmental transfer models neglect the "competitiveness" during the transfer process, that is, the "infection" of people with positive and negative opinions to "susceptibles" or even people with opposing views. To tackle the above issues, in this paper, we propose a novel competitive infectious transmission model in which the "infection" will lead to more people supporting the opinion of the infector, effectively establishing the change of the number of units in the positive, negative, and neutral parties over time. In addition, we performed extensive theoretical analysis to investigate the property of the disease-free equilibrium and to calculate the basic reproduction numbers for three different scenarios. For each system, we derive explicit solutions for the basic reproduction numbers and discuss their important implications for guidance in practice.