We show a simple model of the dynamics of a viral process based, on the determination of the Kaplan-Meier curve P of the virus. Together with the function of the newly infected individuals I, this model allows us to predict the evolution of the resulting epidemic process in terms of the number E of the death patients plus individuals who have overcome the disease. Our model has as a starting point the representation of E as the convolution of I and P. It allows introducing information about latent patients—patients who have already been cured but are still potentially infectious, and re-infected individuals. We also provide three methods for the estimation of P using real data, all of them based on the minimization of the quadratic error: the exact solution using the associated Lagrangian function and Karush-Kuhn-Tucker conditions, a Monte Carlo computational scheme acting on the total set of local minima, and a genetic algorithm for the approximation of the global minima. Although the calculation of the exact solutions of all the linear systems provided by the use of the Lagrangian naturally gives the best optimization result, the huge number of such systems that appear when the time variable increases makes it necessary to use numerical methods. We have chosen the genetic algorithms. Indeed, we show that the results obtained in this way provide good solutions for the model.

中文翻译：

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基于Kaplan-Meier曲线确定的流​​行病演化模型

我们根据病毒的Kaplan-Meier曲线P的确定显示了一个简单的病毒过程动力学模型。结合新感染的个体I的功能，该模型使我们能够根据死亡患者加上已克服疾病的个体E的数量来预测由此流行过程的演变。我们的模型将E表示为I和P的卷积作为起点。它允许引入有关潜在患者的信息，这些患者已经治愈但仍具有潜在感染力，并且已被重新感染。我们还提供了三种估算P的方法使用真实数据，所有这些数据都是基于二次误差的最小化：使用关联的拉格朗日函数和Karush-Kuhn-Tucker条件的精确解，对总局部极小值起作用的蒙特卡洛计算方案以及遗传算法近似于全局最小值。尽管通过使用拉格朗日算式对所有线性系统的精确解的计算自然会得出最佳的优化结果，但是当时间变量增加时出现的此类系统数量巨大，因此有必要使用数值方法。我们选择了遗传算法。实际上，我们表明以这种方式获得的结果为该模型提供了良好的解决方案。