{"title":"具有季节性和空间异质性的反应-平流-扩散血吸虫病流行模型的阈值动力学","authors":"Peng Wu, Yurij Salmaniw, Xiunan Wang","doi":"10.1007/s00285-024-02097-6","DOIUrl":null,"url":null,"abstract":"<p>Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction–advection–diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number <span>\\({\\mathcal {R}}_0\\)</span> and show that the disease-free periodic solution is globally attractive when <span>\\({\\mathcal {R}}_0<1\\)</span> whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when <span>\\({\\mathcal {R}}_0>1\\)</span>. Moreover, we find that <span>\\({\\mathcal {R}}_0\\)</span> is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.\n</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"60 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity\",\"authors\":\"Peng Wu, Yurij Salmaniw, Xiunan Wang\",\"doi\":\"10.1007/s00285-024-02097-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction–advection–diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number <span>\\\\({\\\\mathcal {R}}_0\\\\)</span> and show that the disease-free periodic solution is globally attractive when <span>\\\\({\\\\mathcal {R}}_0<1\\\\)</span> whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when <span>\\\\({\\\\mathcal {R}}_0>1\\\\)</span>. Moreover, we find that <span>\\\\({\\\\mathcal {R}}_0\\\\)</span> is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.\\n</p>\",\"PeriodicalId\":50148,\"journal\":{\"name\":\"Journal of Mathematical Biology\",\"volume\":\"60 1\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Biology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00285-024-02097-6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"BIOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Biology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00285-024-02097-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"BIOLOGY","Score":null,"Total":0}
Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity
Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction–advection–diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number \({\mathcal {R}}_0\) and show that the disease-free periodic solution is globally attractive when \({\mathcal {R}}_0<1\) whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when \({\mathcal {R}}_0>1\). Moreover, we find that \({\mathcal {R}}_0\) is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.
期刊介绍:
The Journal of Mathematical Biology focuses on mathematical biology - work that uses mathematical approaches to gain biological understanding or explain biological phenomena.
Areas of biology covered include, but are not restricted to, cell biology, physiology, development, neurobiology, genetics and population genetics, population biology, ecology, behavioural biology, evolution, epidemiology, immunology, molecular biology, biofluids, DNA and protein structure and function. All mathematical approaches including computational and visualization approaches are appropriate.