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A partially degenerate reaction-diffusion cholera model with temporal and spatial heterogeneity. (English) Zbl 1525.37092

Summary: 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 \(\mathcal{R}_0\) for the model and then show that \(\mathcal{R}_0\) 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 \(\mathcal{R}_0\). It is found that \(\mathcal{R}_0\) is not monotone concerning seasonality for indirect transmission.

MSC:

37N25 Dynamical systems in biology
92D30 Epidemiology
35K57 Reaction-diffusion equations
Full Text: DOI

References:

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