# A novel indicator in epidemic monitoring through a case study of Ebola in West Africa (2014–2016)

## TL;DR

This paper introduces a new indicator, the Cross Point (CP), to monitor epidemics, using the 2014–2016 Ebola outbreak as a case study.

## Contribution

The novel Cross Point (CP) is introduced as an indicator for tracking epidemic dynamics without needing the incubation period.

## Key findings

- The E/S ratio reaches an extremum at the Cross Point (CP), indicating a critical shift in transmission dynamics.
- CP aligns with the time when the reproduction number (Rt) approaches 1, offering a practical monitoring tool.
- Transmission rate curves for different incubation periods intersect at CP, which can be traced over time.

## Abstract

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).