The role of the E/S ratio in the SEIR model: A case study of the Ebola outbreak in West Africa (2014–2016)

Abstract

Abstract In the SEIR model, the role of the E/S ratio in the epidemic model is analyzed. It is shown that transmission rate curves corresponding to various incubation periods cross at a single point denoted by Cross Point (CP), where it satisfies \(\frac{\text{d}}{\text{d}\text{t}}\left(E/S\right)=0\). The time-dependent reproduction number (Rt) approximately reaches 1 at the time of CP. The E/S ratio plays a key role in determining which point between CP and Rt = 1 appears first. As CP can be obtained without knowledge of the incubation period, it can be a useful measure to identify the epidemic status wherein the time-dependent reproduction number is very close to one. As a case study, we estimate the time-dependent transmission rate and the reproduction number of the SEIR model for the 2014–2016 Ebola outbreak in Sierra Leone and Guinea by solving the inverse problem. We identify CP and Rt = 1 and investigate the E/S ratio for various cases of S(0). Mathematics Subject Classification 92-10