# Global Stability of an SEIR Epidemic Model where Empirical Distribution of Incubation Period has Approximated by Coxian Distribution

## TL;DR

This paper introduces a Coxian distributed SEIR epidemic model that incorporates empirical incubation period data, demonstrating that its global dynamics depend solely on the basic reproduction number and offering a flexible approach for realistic epidemic modeling.

## Contribution

The paper develops a Coxian distributed SEIR model that accurately incorporates empirical incubation periods, enhancing classical models' realism and analytical tractability.

## Key findings

- Global dynamics depend on the basic reproduction number.
- Application to empirical data demonstrates model's practical utility.
- Coxian distribution's flexibility allows approximation of various incubation period distributions.

## Abstract

In this work, we have developed a Coxian distributed SEIR model in incorporating an empirical incubation period. We show that the global dynamics are completely determined by a basic reproduction number. An application of the Coxian distributed SEIR model using data of an empirical incubation period is explored. The model may be useful for resolving causing the realistic intrinsic parts in classical epidemic models since Coxian distribution approximately converges to any distribution.