PERIODIC AND ALMOST PERIODIC SOLUTIONS FOR A NON-AUTONOMOUS RESPIRATORY DISEASE MODEL WITH A LAG EFFECT

doi:10.1007/s10473-022-0110-3

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 187-211.doi: 10.1007/s10473-022-0110-3

PERIODIC AND ALMOST PERIODIC SOLUTIONS FOR A NON-AUTONOMOUS RESPIRATORY DISEASE MODEL WITH A LAG EFFECT

石磊, 齐龙兴, 翟素兰

School of Mathematical Sciences, Anhui University, Hefei, 230601, China

收稿日期:2020-07-27 修回日期:2021-05-21 出版日期:2022-02-25 发布日期:2022-02-24
通讯作者: Longxing QI,E-mail:qilx@ahu.edu.cn E-mail:qilx@ahu.edu.cn
作者简介:Lei SHI,E-mail:1325180014@qq.com;Sulan ZHAI,E-mail:sulanzhai@gmail.com
基金资助:
This research was supported by the National Natural Science Foundation of China (11401002, 11771001), the Natural Science Foundation of Anhui Province (2008085MA02), the Natural Science Fund for Colleges and Universities in Anhui Province (KJ2018A0029), the Teaching Research Project of Anhui University (ZLTS2016065), the Quality engineering project of colleges and universities in Anhui Province (2020jyxm0103), and the Science Foundation of Anhui Province Universities (KJ2019A005).

PERIODIC AND ALMOST PERIODIC SOLUTIONS FOR A NON-AUTONOMOUS RESPIRATORY DISEASE MODEL WITH A LAG EFFECT

Lei SHI, Longxing QI, Sulan ZHAI

School of Mathematical Sciences, Anhui University, Hefei, 230601, China

Received:2020-07-27 Revised:2021-05-21 Online:2022-02-25 Published:2022-02-24
Contact: Longxing QI,E-mail:qilx@ahu.edu.cn E-mail:qilx@ahu.edu.cn
Supported by:
This research was supported by the National Natural Science Foundation of China (11401002, 11771001), the Natural Science Foundation of Anhui Province (2008085MA02), the Natural Science Fund for Colleges and Universities in Anhui Province (KJ2018A0029), the Teaching Research Project of Anhui University (ZLTS2016065), the Quality engineering project of colleges and universities in Anhui Province (2020jyxm0103), and the Science Foundation of Anhui Province Universities (KJ2019A005).

摘要/Abstract

摘要： This paper studies a kind of non-autonomous respiratory disease model with a lag effect. First of all, the permanence and extinction of the system are discussed by using the comparison principle and some differential inequality techniques. Second, it assumes that all coefficients of the system are periodic. The existence of positive periodic solutions of the system is proven, based on the continuation theorem in coincidence with the degree theory of Mawhin and Gaines. In the meantime, the global attractivity of positive periodic solutions of the system is obtained by constructing an appropriate Lyapunov functional and using the Razumikin theorem. In addition, the existence and uniform asymptotic stability of almost periodic solutions of the system are analyzed by assuming that all parameters in the model are almost periodic in time. Finally, the theoretical derivation is verified by a numerical simulation.

关键词: respiratory disease, lag effect, periodic solution, almost periodic solution, Lyapunov functional

Abstract: This paper studies a kind of non-autonomous respiratory disease model with a lag effect. First of all, the permanence and extinction of the system are discussed by using the comparison principle and some differential inequality techniques. Second, it assumes that all coefficients of the system are periodic. The existence of positive periodic solutions of the system is proven, based on the continuation theorem in coincidence with the degree theory of Mawhin and Gaines. In the meantime, the global attractivity of positive periodic solutions of the system is obtained by constructing an appropriate Lyapunov functional and using the Razumikin theorem. In addition, the existence and uniform asymptotic stability of almost periodic solutions of the system are analyzed by assuming that all parameters in the model are almost periodic in time. Finally, the theoretical derivation is verified by a numerical simulation.

Key words: respiratory disease, lag effect, periodic solution, almost periodic solution, Lyapunov functional

中图分类号:

34A40

石磊, 齐龙兴, 翟素兰. PERIODIC AND ALMOST PERIODIC SOLUTIONS FOR A NON-AUTONOMOUS RESPIRATORY DISEASE MODEL WITH A LAG EFFECT[J]. 数学物理学报(英文版), 2022, 42(1): 187-211.

Lei SHI, Longxing QI, Sulan ZHAI. PERIODIC AND ALMOST PERIODIC SOLUTIONS FOR A NON-AUTONOMOUS RESPIRATORY DISEASE MODEL WITH A LAG EFFECT[J]. Acta mathematica scientia,Series B, 2022, 42(1): 187-211.

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PERIODIC AND ALMOST PERIODIC SOLUTIONS FOR A NON-AUTONOMOUS RESPIRATORY DISEASE MODEL WITH A LAG EFFECT

PERIODIC AND ALMOST PERIODIC SOLUTIONS FOR A NON-AUTONOMOUS RESPIRATORY DISEASE MODEL WITH A LAG EFFECT

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