A New Family of Time Series to Model the Decreasing Relative Increment of Spreading of an Outbreak

Introduction: There are different mathematical models describing the propagation of an epidemic. These models can be divided into phenomenological, compartmental, deep learning, and individual-based methods. From other viewpoints, we can classify them into macroscopic or microscopic, stochastic or deterministic, homogeneous or heterogeneous, univariate or multivariate, parsimonious or complex, or forecasting or mechanistic. This paper defines a novel univariate bi-partite time series model able to describe spreading a communicable infection in a population in terms of the relative increment of the cumulative number of confirmed cases. The introduced model can describe different stages of the first wave of the outbreak of a communicable disease from the start to the end. Methods: The outcome of the model is relative increment, and it has five positive parameters: the length of the first days of spreading and the relative increment in these days, the potent of the mildly decreasing trend (after the significant decrease), and the adjusting coefficient to adapt this trend to the initial pattern, and the fixed ratio of the mean to the variance. Results: We use it to describe the propagation of various disease outbreaks, including the SARS (2003), the MERS (2018), the Ebola (2014-2016), the HIV/AIDS (1990-2018), the Cholera (2008-2009), and the COVID-19 epidemic in Iran, Italy, the UK, the USA, China and four of its provinces; Beijing, Guangdong, Shanghai, and Hubei (2020). In all mentioned cases, the model has an acceptable performance. In addition, we compare the goodness of this model with the ARIMA models by fitting the propagation of COVID-19 in Iran, Italy, the UK, and the USA. Conclusion: The introduced model is flexible enough to describe a broad range of epidemics. In comparison with ARIMA time series models, our model is more initiative and less complicated, it has fewer parameters, the estimation of its parameters is more straightforward, and its forecasts are narrower and more accurate. Due to its simplicity and accuracy, this model is a good tool for epidemiologists and biostatisticians to model the first wave of an epidemic.