The Effects of Migration and Limited Medical Resources of the Transmission of SARS-CoV-2 Model with Two Patches

• Published in: Bulletin of mathematical biology Vol. 84; no. 5; p. 55
• Main Authors: Hu, Lin, Wang, Shengfu, Zheng, Tingting, Hu, Zhenxiang, Kang, Yuenan, Nie, Lin-Fei, Teng, Zhidong
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2022; Springer Nature B.V
• Subjects: Asymptomatic; Basic Reproduction Number; Cell Biology; COVID-19 - epidemiology; Developing countries; Disease control; Disease transmission; Humans; LDCs; Liapunov functions; Life Sciences; Mathematical and Computational Biology; Mathematical Concepts; Mathematical models; Mathematics; Mathematics and Statistics; Models, Biological; Patches (structures); SARS-CoV-2; Severe acute respiratory syndrome coronavirus 2; Special Issue: Mathematics and Covid-19; Viral diseases; Threshold value; SARS-CoV-2 model; Bifurcation and stability; Limited medical resources and migration
• ISSN: 0092-8240; 1522-9602
• DOI: 10.1007/s11538-022-01010-w

The sudden outbreak of SARS-CoV-2 has caused the shortage of medical resources around the world, especially in developing countries and underdeveloped regions. With the continuous increase in the duration of this disease, the control of migration of humans between regions or countries has to be relaxed. Based on this, we propose a two-patches mathematical model to simulate the transmission of SARS-CoV-2 among two-patches, asymptomatic infected humans and symptomatic infected humans, where a half-saturated detection rate function is also introduced to describe the effect of medical resources. By applying the methods of linearization and constructing a suitable Lyapunov function, the local and global stability of the disease-free equilibrium of this model without migration is obtained. Further, the existence of forward/backward bifurcation is analyzed, which is caused by the limited medical resources. This means that the elimination or prevalence of the disease no longer depends on the basic reproduction number but is closely related to the initial state of asymptomatic and symptomatic infected humans and the supply of medical resources. Finally, the global dynamics of the full model are discussed, and some numerical simulations are carried to explain the main results and the effects of migration and supply of medical resources on the transmission of disease.