Abstract
Cholera remains a significant threat to public health and economics. Although various mathematical models published in recent years have made an essential contribution to the study of cholera outbreaks, their dynamics are still not fully understood. To study the temporal-spatial dynamics of cholera spread, we propose a partially degenerate reaction–diffusion cholera model, which allows for the transmission rate and the shedding rate of cholera bacteria varying explicitly with both time and space. We define the basic reproduction number for the model and then show that acts as a threshold parameter determining whether or not the disease can invade a population. Numerically, we investigate the influences of diffusion rate, seasonality, and heterogeneity on . It is found that is not monotone concerning seasonality for indirect transmission.
Acknowledgments
We sincerely thank Dr. Lei Zhang for helpful discussions on the definition of . We are also grateful to two anonymous referees for careful reading and insightful comments which led to improvements of our original manuscript.
Disclosure statement
No potential conflict of interest was reported by the authors.