Asymptotic profile of the solution to a diffusive cholera epidemic model with free boundaries

Cholera remains a significant global public health challenge, highlighting the necessity for a more comprehensive understanding of its transmission and control mechanisms. This paper investigates a cholera epidemic model based on a reaction-diffusion system with free boundaries, which effectively captures the spread of the disease through an expanding front. We focus on the long-term behavior of the system, proving that the spreading fronts of the epidemic are well-approximated by a linear function with finite error. Additionally, we demonstrate that the solution to the free boundary problem eventually evolves into a semi-wave solution, providing valuable insights into the asymptotic dynamics of cholera spread. These results contribute to a deeper understanding of the diffusion process in cholera epidemics and have significant implications for designing targeted intervention strategies.