Alternative procedure to calculate the basic reproduction number

To control and manage the different waves of an endemic or epidemic disease, it is useful to know how quickly the contagious disease spreads. Two dimensionless numbers the basic (R_o) and effective (R_e) reproduction numbers, provide such information. Furthermore, compartmental models are frequently employed in epidemiology to mimic infectious-disease dynamics. A review of the literature indicates that the next-generation matrix (NGM) method is the only approach used to obtain an analytical expression for the basic reproduction number (R_o). In this study, we aim to demonstrate a simpler, non-trivial procedure for calculating R_o in a closed form. The rationale for this undertaking is threefold. First, it provides an independent procedure to obtain the analytical value of R_o. Second, the proposed alternative procedure uses basic algebra, whereas the standard method (NGM) requires linear algebra. Third, the alternative method can be used to easily explain why R_o >1, implies an endemic disease. Finally, as an application we estimate the R_o and R_e values for Puerto Rico during the 2020 pandemic.