Traveling wave solutions of a susceptible-infectious model

This paper studies the traveling wave solutions of a susceptible and infectious (SI) mathematical model with and without recruitment rates. Our research provides numerical solutions for the proposed models, confirming the existence of traveling wave solutions. We meticulously calculate the minimal traveling wave speeds and analytically determine the spreading speed without turnover for the susceptible population. The paper also investigates the relationship between the spreading speeds and the model parameters. Additionally, we identify the threshold density of susceptible individuals, a crucial point below which the disease cannot persist. Our findings also confirm that the disease ceases to exist if the death rates surpass the rate of new cases of infections.