A Convex Optimization Solution for the Effective Reproduction Number

COVID-19 is a global infectious disease that has affected millions of people. With new variants emerging with augmented transmission rates, slowing down of vaccine rollouts, and rising new cases threatening sanitary capabilities to the brink of collapse, there is the need to continue studying more effective forms to track its spread. This paper presents a strategy to compute the effective reproduction number Rt. Our method starts with a form of the renewal equation of the birth process specially suitable to compute Rt. After showing that one can express it as a linear system, we proceed to solve it, along with appropriate constraints, using convex optimization. We demonstrate the method’s effectiveness using synthetic and real sequences of infections and comparing it with a leading approach.