The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model
The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model
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DOI：
10.1016/s0167-2789(02)00389-5
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发表时间：
2002-05-15
影响因子：
4
通讯作者：
Sasaki, A
中科院分区：
文献类型：
--
作者：
Kamo, M;Sasaki, A
研究了一类具有季节性传染率强迫的多菌株SIR流行病模型的动力学行为和分支结构。传统的单应变SIR动力学与季节性强迫是已知的，表现出一系列的分歧的强度的季节性增加。在这项研究中，我们扩展到多个菌株的病原体，首先调查的分歧模式的两个菌株SIR模型。在两个应变SIR模型中，应变间的交叉免疫性是影响其动力学行为的重要参数。与单应变模式类似，我们发现随着季节强迫强度的增加，会出现倍周期分岔。然而，分叉模式在它们的次谐波周期和菌株之间的周期的相对相位上都有很大的不同，这主要取决于菌株之间的交叉免疫的程度。在强、弱交叉免疫的情况下，倍周期级联逐渐走向混沌循环。另一方面，与中间交叉免疫，年周期吸引子的稳定性的损失是紧随其后的混沌周期。当年周期失去稳定性时，两个菌株的异步周期是稳健的结果，但是如果两个菌株在抗原性上彼此远离，则种群可以收敛到完全同步的两年周期。其次，我们发现两应变SIR模型存在同时稳定的多个吸引子。两年期和混沌吸引子，例如，有时候它们会以相同程度的季节强迫共存，根据初始条件，轨迹会收敛到其中一个。这种多重吸引子广泛存在于两年周期和年周期之间，或者不同类型的两年周期之间，具有相同的季节性强度。最后，我们发现，人口可以从一个吸引到另一个通过引入一个小的随机噪声在季节性变化的传输率。(C)2002 Elsevier Science B.V.保留所有权利。
study dynamical behavior and bifurcation structure of a multi-strain SIR epidemiological model with seasonal forcing in transmission rate. The conventional single strain SIR dynamics with seasonal forcing is known to show a cascade of bifurcations as the strength of seasonality increases. In this study with an extension to multiple strains of pathogens, we first investigate the bifurcation patterns of the two strain SIR model. In the two strain SIR model, a new parameter called cross-immunity between strains plays a key role in the dynamical behavior. As analogous to the single strain model, we found that the period doubling bifurcation occurs as the strength of seasonal forcing is increased. However, bifurcation patterns differ greatly both in their subharmonic periods and the relative phase of cycles between strains, depending mostly on the degree of the cross-immunity between strains. With strong and weak cross-immunities, the period doubling cascade proceeds gradually toward chaotic cycles. On the other hand, with intermediate cross-immunity, the loss of stability of annual cycle attractor is immediately followed by chaotic cycles. Asynchronous cycles of two strains are robust outcome when annual cycles lose stability, but the population can converge to perfectly synchronized biennial cycles if two strains are antigenically distant from each other. Second, we found that there are simultaneously stable multiple attractors in two strain SIR model. Biennial and chaotic attractors, e.g., occasionally coexist at the same degree of seasonal forcing, and the trajectories converge to one of them depending on the initial conditions. Such multiple attractors are widely seen between biennial and annual cycles, or among the different types of biennial cycles, at the same strength of the seasonality. Finally, we found that the population may switch from one attractor to another by introducing a small random noise in seasonally varying transmission rate. (C) 2002 Elsevier Science B.V. All rights reserved.