群体作用的化学反应定义在传染病建模中的应用

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2020-03-23 DOI:10.5206/mase/9372
M. Al-arydah, S. Greenhalgh, J. Munganga, Robert J. Smith
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引用次数: 1

摘要

质量作用定律用于控制各种传染病模型中易感个体和受感染个体之间的相互作用。然而,通常使用的版本是最初用于描述化学反应的版本的简化。我们使用质量作用的化学反应定义,将改变的传播项和改变的恢复项以正指数的形式结合起来,重新制定了一般疾病模型。我们考察了这些指数变化的长期结果。在许多情况下,复制数要么为0,要么为$\infty$,而它仅对某些组合获得有限值。我们发现了地方性平衡存在的条件,并且对各种可能的指数都是唯一的。我们还确定了可能发生或不发生后向分岔的情况。质量作用的简化形式可能掩盖了如果这些指数在1附近“波动”可能导致的一般行为。这可能导致某些模型失去可预测性。
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Applying the chemical-reaction definition of mass action to infectious disease modelling
The law of mass action is used to govern interactions between susceptible and infected individuals in a variety of infectious disease models. However, the commonly used version is a simplification of the version originally used to describe chemical reactions. We reformulate a general disease model using the chemical-reaction definition of mass action incorporating both an altered transmission term and an altered recovery term in the form of positive exponents. We examine the long-term outcome as these exponents vary. For many scenarios, the reproduction number is either 0 or $\infty$, while it obtains finite values only for certain combinations. We found conditions under which endemic equilibria exist and are unique for a variety of possible exponents. We also determined circumstances under which backward bifurcations are possible or do not occur. The simplified form of mass action may be masking generalised behaviour that may result in practice if these exponents ``fluctuate'' around 1. This may lead to a loss of predictability in some models.
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
0
审稿时长
21 weeks
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