# Global Stability of a Mumps Transmission Model with Quarantine Measure

Global Stability of a Mumps Transmission Model with Quarantine Measure In this paper, a model of mumps transmission with quarantine measure is proposed and then the control reproduction number ℛc\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\cal R}_c}$$\end{document} of the model is obtained. This model admits a unique endemic equilibrium P* if and only if Rc > 1, while the disease-free equilibrium P0 always exists. By using the technique of constructing Lyapunov functions and the generalized Lyapunov-LaSalle theorem, we first show that the equilibrium P0 is globally asymptotically stable (GAS) if Rc ≤ 1; second, we prove that the equilibrium P* is GAS if Rc > 1. Our results reveal that mumps can be eliminated from the community for ℛc≤1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\cal R}_c} \le 1$$\end{document} and it will be persistent for ℛc>1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\cal R}_c} > 1$$\end{document}, and quarantine measure can also effectively control the mumps transmission. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Global Stability of a Mumps Transmission Model with Quarantine Measure

, Volume 37 (4) – Oct 1, 2021
8 pages

/lp/springer-journals/global-stability-of-a-mumps-transmission-model-with-quarantine-measure-wDl48t0aHE
Publisher
Springer Journals
Copyright © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2021
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-021-1035-7
Publisher site
See Article on Publisher Site

### Abstract

In this paper, a model of mumps transmission with quarantine measure is proposed and then the control reproduction number ℛc\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\cal R}_c}$$\end{document} of the model is obtained. This model admits a unique endemic equilibrium P* if and only if Rc > 1, while the disease-free equilibrium P0 always exists. By using the technique of constructing Lyapunov functions and the generalized Lyapunov-LaSalle theorem, we first show that the equilibrium P0 is globally asymptotically stable (GAS) if Rc ≤ 1; second, we prove that the equilibrium P* is GAS if Rc > 1. Our results reveal that mumps can be eliminated from the community for ℛc≤1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\cal R}_c} \le 1$$\end{document} and it will be persistent for ℛc>1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\cal R}_c} > 1$$\end{document}, and quarantine measure can also effectively control the mumps transmission.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Oct 1, 2021

Keywords: mumps transmission model; control reproduction number; quarantine measure; global stability; 34D23; 37N25; 92D30