Abstract：
The bacteria Vibrio cholerae relies heavily upon an aquatic reservoir as a transmission route with two distinct serotypes observed in many recent outbreaks. In this paper, we extend previously studied ordinary differential equation epidemiological models to create a two-strain SIRP (susceptible-infectious-recovered-pathogen) system which incorporates both partial cross-immunity between disease strains and environmental pathogen transmission. Of particular interest are undamped anti-phase periodic solutions, as these display a type of coexistence where strains routinely switch dominance, and understanding what drives this switch can optimize the efficiency of the host population\'s control measures against the disease. We derive the basic reproduction number R0 and use stability analysis to examine the disease free and single-strain equilibria. We formulate a unique coexistence equilibrium and prove uniform persistence of both strains when R0>1. In addition, we simulate solutions to this system, along with seasonally forced versions of the model with and without host coinfection. Cross-immunity and transmission pathways influence damped or sustained oscillatory dynamics, where the presence of seasonality can modify, amplify or synchronize the period and phase of serotypes, driving epidemic waves. Cycling of serotypes over large time intervals, similar to observed data, is found for a range of cross-immunity levels, and the inclusion of coinfection in the model contributes to sustained anti-phase periodic solutions.
摘要：
霍乱弧菌严重依赖水生水库作为传播途径，在最近的许多疫情中观察到两种不同的血清型。在本文中,我们扩展了先前研究的常微分方程流行病学模型,以创建一个两菌株SIRP(易感感染-恢复病原体)系统,该系统同时包含疾病菌株和环境病原体传播之间的部分交叉免疫.特别感兴趣的是无阻尼反相位周期解，因为这些表现出一种共存的类型，菌株通常会切换主导地位，了解是什么推动了这种转变，可以优化宿主群体对疾病的控制措施的效率。我们得出基本繁殖数R0，并使用稳定性分析来检查无病和单菌株平衡。我们制定了独特的共存平衡，并证明了当R0>1时两种菌株的均匀持久性。此外,我们模拟这个系统的解决方案，以及有和没有宿主共感染的模型的季节性强制版本。交叉免疫和传播途径影响阻尼或持续振荡动力学，季节性的存在可以改变，扩增或同步血清型的周期和阶段，推动流行病浪潮。在大的时间间隔内循环血清型，与观察到的数据相似，发现了一系列交叉免疫水平，并且在模型中包含共感染有助于持续的反相位周期解。
