Permanence and Uniform Asymptotic Stability of Positive Solutions of SAIQH Models on Time Scales

TL;DR

This paper introduces a SAIQH epidemiological model on time scales, proving its permanence, existence of solutions, and conditions for a unique, uniformly asymptotically stable almost periodic solution, supported by an example.

Contribution

It develops a novel SAIQH model on time scales and establishes stability and permanence results using Lyapunov functions, advancing the mathematical understanding of such models.

Findings

The system is permanent.

Existence of solutions is proven.

Conditions for a unique, stable almost periodic solution are provided.

Abstract

A susceptible, asymptomatic, infectious, quarantined, and hospitalized (SAIQH) compartmental model on time scales is introduced and a suitable Lyapunov function is defined. Main results include: the proof that the system is permanent; proof of existence of solution; and sufficient conditions implying the dynamic system to have a unique almost periodic solution that is uniformly asymptotically stable. An example is presented supporting the obtained results.