The E/S (exposed/susceptible) ratio is analyzed in the SEIR model. The ratio plays a key role in understanding epidemic dynamics during the 2014-2016 Ebola outbreak in Sierra Leone and Guinea. The maximum value of the ratio occurs immediately before or after the time-dependent reproduction number (Rt) equals 1, depending on the initial susceptible population (S(0)). It is demonstrated that transmission rate curves corresponding to various incubation periods intersect at a single point referred to as the Cross Point (CP). At this point, the E/S ratio reaches an extremum, signifying a critical shift in transmission dynamics and aligning with the time when Rt approaches 1. By plotting transmission rate curves, β(t), for any two arbitrary incubation periods and tracking their intersections, we can trace CP over time. CP serves as an indicator of epidemic status, especially when Rt is close to 1. It provides a practical means of monitoring epidemics without prior knowledge of the incubation period. Through a case study, we estimate the transmission rate and reproduction number, identifying CP and Rt = 1 while examining the E/S ratio across various values of S(0).

UNASSIGNED: Mumps is a seasonal infectious disease, always occurring in winter and spring. In this study, we aim to analyze its epidemiological characteristics, transmissibility, and its correlation with meteorological variables.
UNASSIGNED: A seasonal Susceptible-Exposed-Infectious/Asymptomatic-Recovered model and a next-generation matrix method were applied to estimate the time-dependent reproduction number (R t ).
UNASSIGNED: The seasonal double peak of annual incidence was mainly in May to July and November to December. There was high transmission at the median of R t  = 1.091 (ranged: 0 to 4.393). R t was seasonally distributed mainly from February to April and from September to November. Correlations were found between temperature (Pearson correlation coefficient [r] ranged: from 0.101 to 0.115), average relative humidity (r = 0.070), average local pressure (r = -0.066), and the number of new cases. In addition, average local pressure (r = 0.188), average wind speed (r = 0.111), air temperature (r ranged: -0.128 to -0.150), average relative humidity (r = -0.203) and sunshine duration (r = -0.075) were all correlated with R t .
UNASSIGNED: A relatively high level of transmissibility has been found in Xiamen City, leading to a continuous epidemic of mumps. Meteorological factors, especially air temperature and relative humidity, may be more closely associated with mumps than other factors.