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

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 (R t ) approximately reaches 1 at the time of CP. The E / S ratio plays a key role in determining which point between CP and R t = 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 R t = 1 and investigate the E / S ratio for various cases of S(0). Mathematics Subject Classification 92-10