Discrete spread model for COVID‐19: the case of Lebanon

Mathematical models are essential to predict the likely outcome of an epidemic. Various models have been proposed in the literature for disease spreads. Some are individual based models and others are compartmental models. In this study, discrete mathematical models are developed for the spread of the coronavirus disease 2019 (COVID‐19). The proposed models take into account the known special characteristics of this disease such as the latency and incubation periods, and the different social and infectiousness conditions of infected people. In particular, they include a novel approach that considers the social structure, the fraction of detected cases over the real total infected cases, the influx of undetected infected people from outside the borders, as well as contact‐tracing and quarantine period for travelers. The first model is a simplified model and the second is a complete model. From a numerical point of view, the particular case of Lebanon has been studied and its reported data have been used to estimate the complete discrete model parameters using optimization techniques. Moreover, a parameter analysis and several prediction scenarios are presented in order to better understand the role of the parameters. Understanding the role of the parameters involved in the models help policy makers in deciding the appropriate mitigation measures. Also, the proposed approach paves the way for models that take into account societal factors and complex human behavior without an extensive process of data collection. Author summary:Mathematical models use mathematical concepts to describe systems. In epidemiology, models try for instance to predict the evolution of the number of infected in the population or the duration of an epidemic. Such models can show how different public health interventions may affect the outcome of the epidemic. A class of existing models consists of ordinary differential equations that are based on the assumption of homogeneous mixing of the population. To be more realistic, we propose herein two discrete models that take into account heterogeneities in the population such as the social activity level of individuals.