与SEIR流行病模型相关的一组微分方程波的精确形式的计算

N. Vitanov, Z. Dimitrova
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引用次数: 2

摘要

我们研究了流行病传播的SEIR(易感-暴露-感染-恢复)模型的一组方程的精确解。这些解决方案可用于模拟流行病波。我们将SEIR模型转化为包含指数非线性的微分方程。然后用一组包含多项式非线性的微分方程来近似这个方程。我们用简单方程法(SEsM)从集合中求解了几个方程。通过这样做,我们得到了相应方程的许多新的精确解。其中一些解决方案可以描述影响人口中一小部分个体的流行病波的演变。近年来,在COVID-19大流行中经常观察到这种波动。讨论表明,SEsM是计算非线性微分方程精确解的有效方法。得到的精确解可以帮助我们理解模型系统中各种过程的演化。在SEIR模型的具体案例中,一些精确的解可以帮助我们更好地理解与流行病波相关的量的演变。
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Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics
We studied obtaining exact solutions to a set of equations related to the SEIR (Susceptible-Exposed-Infectious-Recovered) model of epidemic spread. These solutions may be used to model epidemic waves. We transformed the SEIR model into a differential equation that contained an exponential nonlinearity. This equation was then approximated by a set of differential equations which contained polynomial nonlinearities. We solved several equations from the set using the Simple Equations Method (SEsM). In doing so, we obtained many new exact solutions to the corresponding equations. Several of these solutions can describe the evolution of epidemic waves that affect a small percentage of individuals in the population. Such waves have frequently been observed in the COVID-19 pandemic in recent years. The discussion shows that SEsM is an effective methodology for computing exact solutions to nonlinear differential equations. The exact solutions obtained can help us to understand the evolution of various processes in the modeled systems. In the specific case of the SEIR model, some of the exact solutions can help us to better understand the evolution of the quantities connected to the epidemic waves.
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