This work introduces a new markovian stochastic model that can be described as a non-homogeneous Pure Birth process. We propose a functional form of birth rate that depends on the number of individuals in the population and on the elapsed time, allowing us to model a contagion effect. Thus, we model the early stages of an epidemic. The number of individuals then becomes the infectious cases and the birth rate becomes the incidence rate. We obtain this way a process that depends on two competitive phenomena, infection and immunization. Variations in those rates allow us to monitor how effective the actions taken by government and health organizations are. From our model, three useful indicators for the epidemic evolution over time are obtained: the immunization rate, the infection/immunization ratio and the mean time between infections (MTBI). The proposed model allows either positive or negative concavities for the mean value curve, provided the infection/immunization ratio is either greater or less than one. We apply this model to the present SARS-CoV-2 pandemic still in its early growth stage in Latin American countries. As it is shown, the model accomplishes a good fit for the real number of both positive cases and deaths. We analyze the evolution of the three indicators for several countries and perform a comparative study between them. Important conclusions are obtained from this analysis.

这项工作引入了一个新的马尔可夫随机模型，可以描述为非均匀纯出生过程。我们提出了一种出生率的函数形式，它取决于人口中的个体数量和经过的时间，从而使我们能够模拟传染效应。因此，我们为流行病的早期阶段建模。然后，个体数量成为感染病例，出生率成为发病率。我们通过这种方式获得了一个过程，该过程取决于两个竞争现象，即感染和免疫。这些费率的变化使我们能够监测政府和卫生组织采取的行动的有效性。从我们的模型中，获得了三个随时间变化的流行趋势的有用指标：免疫率，感染/免疫比和平均感染间隔时间（MTBI）。如果感染/免疫比大于或小于1，则建议的模型允许平均值曲线为正凹或负凹。我们将此模型应用于目前仍处于拉丁美洲国家早期发展阶段的SARS-CoV-2大流行。如图所示，该模型非常适合阳性病例和死亡的真实数目。我们分析了三个国家的三个指标的演变并进行了比较研究。从此分析中得出重要结论。该模型非常适合阳性病例和死亡病例的真实数量。我们分析了三个国家的三个指标的演变并进行了比较研究。从此分析中得出重要结论。该模型非常适合阳性病例和死亡病例的真实数量。我们分析了三个国家的三个指标的演变并进行了比较研究。从此分析中得出重要结论。