{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:41:02Z","timestamp":1776397262425,"version":"3.51.2"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T00:00:00Z","timestamp":1756944000000},"content-version":"vor","delay-in-days":246,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>The human cardiovascular and respiratory systems are critical and appealing study areas, as cardiovascular and respiratory disorders become more prevalent and burdensome for families. This paper is aimed at developing a mathematical model with delays for determining blood pressure\u2019s response to cardiac and respiratory parameters. Two nonlinear coupled ordinary differential equations are created with the intention of looking for the behavior of the model in stable, unstable, and Hopf bifurcation solutions for mathematical models of arterial and venous pressures during physical activity (rest, walking, jogging, and running cases). A comprehensive mathematical model integrating cardiovascular and respiratory systems, with a focus on delay effects, is necessary to account for physiological response lags between oxygen demand, heart rate, and ventilation rate. A mathematical model representing the mass balance between the systemic arterial and systemic venous compartments has been developed. We also carried out a stability analysis with different delays. The findings reveal that when a delay exceeds a threshold value, we have Hopf bifurcation, and as delays increase, the time lag between changes in systemic arterial and systemic venous pressures increases, resulting in a loss of stability. The results show that the model can accurately predict cardiovascular and respiratory responses and provide insights into system stability and adaptability across exercise intensities. This work advances our understanding of cardiorespiratory dynamics and establishes a framework for individualized health monitoring and activity planning.<\/jats:p>","DOI":"10.1155\/jama\/5920790","type":"journal-article","created":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T10:52:28Z","timestamp":1756983148000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mathematical Modeling of the Cardiovascular and Respiratory Systems With Delay Effects: Case of a 30\u2010Year\u2010Old Woman in Resting, Walking, Jogging, and Running"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0632-2062","authenticated-orcid":false,"given":"Edouard","family":"Singirankabo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean Marie","family":"Ntaganda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vedaste","family":"Mutarutinya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edouard","family":"Diouf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,9,4]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.09.016"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1967.22.2.260"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.5811"},{"key":"e_1_2_10_4_2","volume-title":"A Global Model of the Cardiovascular and Respiratory System","author":"Timischl S.","year":"1998"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:CARE.0000025120.30148.7a"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1152\/ajpregu.00430.2017"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.3389\/fphys.2016.00189"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1051\/mmnp\/20127506"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-004-0293-3"},{"key":"e_1_2_10_10_2","article-title":"Modeling the Human Cardiovascular-Respiratory Control System: An Optimal Control Application to the Transition to Non-REM Sleep","author":"Teschl S.","year":"2000","journal-title":"Journal of Mathematical Biology"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s002850000044"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-024-02718-2"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-024-09438-6"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.3934\/dcdss.2024036"},{"key":"e_1_2_10_15_2","volume-title":"Complex Analysis: The Argument Principle in Analysis and Topology","author":"Beardon A. 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