# Global dynamics of a periodic SEIRS model with general incidence rate

## TL;DR

This paper analyzes a family of periodic SEIRS epidemic models with general incidence rates, demonstrating that the basic reproduction number governs the global dynamics and persistence of the disease, supported by numerical simulations.

## Contribution

It introduces a general periodic SEIRS model with nonlinear incidence rates and establishes the basic reproduction number as a threshold for disease persistence and global behavior.

## Key findings

- Basic reproduction number determines global dynamics.
- Numerical simulations validate analytical results.
- Model accommodates general nonlinear incidence rates.

## Abstract

We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate and it is shown the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence. Numerical simulations are per- formed to estimate the basic reproduction number and illustrate our analytical findings, using a nonlinear incidence rate.