Dynamics of a partially degenerate reaction-diffusion cholera model with horizontal transmission and phage-bacteria interaction

Abstract

We propose a cholera model with coupled reaction-diffusion equations and ordinary differential equations for discussing the effects of spatial heterogeneity, horizontal transmission, environmental viruses and phages on the spread of vibrio cholerae. We establish the well-posedness of this model which includes the existence of unique global positive solution, asymptotic smoothness of semiflow, and existence of a global attractor. The basic reproduction number R0 is obtained to describe the persistence and extinction of the disease. That is, the disease-free steady state is globally asymptotically stable for R0≤1, while it is unstable for R0>1. And, the disease is persistence and the model has the phage-free and phage-present endemic steady states in this case. Further, the global asymptotic stability of phage-free and phage-present endemic steady states are discussed for spatially homogeneous model. Finally, some numerical examples are displayed in order to illustrate the main theoretical results and our opening questions.

A study on predicting the results of Wordle guessing game based on time series and linear regression

“…However, the number of daily active users of Wordle has been decreasing in recent years. Therefore, in this paper, based on the data provided on Twitter, which is assumed to be real, reliable, valid and without machine involvement, we build mathematical models to predict and explain the reasons for the change in the number of reported results [1] and create a prediction interval for the number of reported results on March 1, 2023 [2] [3] . And consider whether the percentage of reported scores performed in Difficult mode is affected by any of the attributes of the words.…”