{"id":17,"date":"2016-09-05T00:47:01","date_gmt":"2016-09-05T04:47:01","guid":{"rendered":"https:\/\/sciencescosmaincms.cm.ucf.edu\/math\/zshuai\/?page_id=17"},"modified":"2024-10-28T18:03:18","modified_gmt":"2024-10-28T22:03:18","slug":"research","status":"publish","type":"page","link":"https:\/\/sciences.ucf.edu\/math\/zshuai\/research\/","title":{"rendered":"Research \/ Publications"},"content":{"rendered":"<h1><strong>Research Highlights<\/strong><\/h1>\n<ul>\n<li>A graph-theoretic approach to the construction of Lyapunov functions for large-scale differential equation systems<br \/>\n<b><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/graph\/\">references<\/a><\/b><\/li>\n<li>Target reproduction numbers with application to ecology and epidemiology<br \/>\n<b><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/target\/\">references<\/a><\/b><\/li>\n<li>Mathematical modeling of waterborne diseases such as <a href=\"http:\/\/www.choleraandthethames.co.uk\/cholera-in-london\/origins-of-cholera\/\">cholera<\/a><\/li>\n<li><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/team\">Research team<\/a> at UCF<\/li>\n<li><a href=\"http:\/\/www.oakland.edu\/enp\/\">Erd\u00f6s number<\/a> = 2 (<a href=\"https:\/\/mathscinet.ams.org\/mathscinet\/freetools\/collab-dist?source=710952&amp;target=189017\">Paul Erd\u0151s coauthored with John Moon, who is also my coauthor<\/a>)<\/li>\n<\/ul>\n<hr \/>\n<h2><strong>Publications<\/strong> \u00a0<a href=\"http:\/\/scholar.google.com\/citations?user=6bIr7oUAAAAJ\">Google Scholar<\/a><\/h2>\n<ul>\n<li>Spectral monotonicity of perturbed quasi-positive matrices with applications in population dynamics (with S. Chen, J. Shi and Y. Wu).<br \/>\n<em>SIAM Journal on Applied Mathematics, <\/em>82 (2022), 654-676. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2023\/02\/2022siap.pdf\">pdf<\/a><\/li>\n<li>Global dynamics of a Lotka-Volterra competition patch model (with S. Chen, J. Shi and Y. Wu).<br \/>\n<em>Nonlinearity<\/em>, 35 (2022), 817-842. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2023\/02\/2022nonl.pdf\">pdf<\/a><\/li>\n<li>Impact of varying community networks on disease invasion (with S. Kirkland, P. van den Driessche and X. Wang).<br \/>\n<em>SIAM Journal on Applied Mathematics<\/em>, 81 (2021), 1166-1189. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2023\/02\/2021siap.pdf\">pdf<\/a> <strong><br \/>\nHighlighted as a Research Nugget of <em>SIAM News<\/em><\/strong>, <a href=\"https:\/\/sinews.siam.org\/Details-Page\/changing-community-networks-impact-disease-spread\">Changing Community Networks Impact Disease Spread<\/a>, June 10, 2021.<br \/>\nAlso see the <a href=\"https:\/\/www.news-medical.net\/news\/20210610\/Changes-in-community-networks-impact-the-ensuing-spread-of-disease.aspx\">News Medical Report<\/a><\/li>\n<li>A mathematical model for vibrio-phage interactions (with C.G. Botelho, J.D. Kong, M.A.B. Lucien and H. Wang).<br \/>\n<em>Mathematical Biosciences and Engineering<\/em>, 18 (2021), 2688-2712. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2023\/02\/2021mbe.pdf\">pdf<\/a><\/li>\n<li>Asymptotic profiles of the steady states for an SIS epidemic patch model with asymmetric connectivity matrix (with S. Chen, J. Shi and Y. Wu).<br \/>\n<em>Journal of Mathematical Biology<\/em>, 80 (2020), 2327-2361. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2023\/02\/2020jmb.pdf\">pdf<\/a><\/li>\n<li>A general theory for target reproduction numbers with applications to ecology and epidemiology (with M.A. Lewis and P. van den Driessche).<br \/>\n<em>Journal of Mathematical Biology<\/em>, 78 (2019), 2317-2339. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2023\/02\/2019jmb.pdf\">pdf<\/a><\/li>\n<li>A mathematical model of syphilis transmission in an MSM population\u00a0(with C.M. Saad-Roy and P. van den Driessche).<br \/>\n<cite>Mathematical Biosciences,<\/cite>\u00a0<strong>277<\/strong> (2016) 59-70. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2017\/04\/2016mbs.pdf\">pdf<\/a><\/li>\n<li>Disease invasion risk in a growing population\u00a0(with S. Yuan, P. van den Driessche, F. Willeboordse and J. Ma).<br \/>\n<cite>Journal of Mathematical Biology,<\/cite>\u00a0<strong>73<\/strong> (2016) 665-681. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2023\/02\/2016jmb.pdf\">pdf<\/a><\/li>\n<li>Models of Bovine Babesiosis including juvenile cattle (with C.M. Saad-Roy and P. van den Driessche).<br \/>\n<cite>Bulletin of Mathematical Biology,<\/cite>\u00a0<strong>77<\/strong> (2015) 514-547. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2017\/04\/2015bmb.pdf\">pdf<\/a><\/li>\n<li>Disease invasion on community networks with environmental pathogen movement (with J.H. Tien, M.C. Eisenberg, and P. van den Driessche).<br \/>\n<cite>Journal of Mathematical Biology,<\/cite>\u00a0<strong>70<\/strong> (2015) 1065-1092. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2017\/04\/2015jmb.pdf\">pdf<\/a><\/li>\n<li>Modelling and control of cholera on networks with a common water source (with P. van den Driessche).<br \/>\n<cite>Journal of Biological Dynamics,<\/cite>\u00a0<strong>9<\/strong> (2015) 90-103. <a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2023\/02\/2015jbd.pdf\">pdf<\/a><\/li>\n<li>Walks and cycles on a digraph with application to population dynamics (with J.W. Moon and P. van den Driessche).<br \/>\n<cite>Linear Algebra and its Applications,<\/cite> <b>451<\/b> (2014) 182-196. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2014laa.pdf\">pdf<\/a><\/strong><\/li>\n<li>A cholera model in a patchy environment with water and human movement (with M.C. Eisenberg, J.H. Tien, and P. van den Driessche).<br \/>\n<cite>Mathematical Biosciences,<\/cite> <b>246<\/b> (2013) 105-112. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2013mbs.pdf\">pdf<\/a><\/strong><\/li>\n<li>Global stability of infectious disease models using Lyapunov functions (with P. van den Driessche).<br \/>\n<cite>SIAM Journal on Applied Mathematics,<\/cite> <b>73<\/b> (2013) 1513-1532. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2013siap.pdf\">pdf<\/a><\/strong><\/li>\n<li>Dynamics of an age-of-infection cholera model (with F. Brauer and P. van den Driessche).<br \/>\n<cite>Mathematical Biosciences and Engineering,<\/cite> <b>10<\/b> (2013) 1335-1349. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2013mbe.pdf\">pdf<\/a><\/strong><\/li>\n<li>Extending the type reproduction number to infectious disease control targeting contacts between types (with J.A.P. Heesterbeek and P. van den Driessche).<br \/>\n<cite>Journal of Mathematical Biology,<\/cite> <b>67<\/b> (2013) 1067-1082. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2023\/02\/2013jmb.pdf\">pdf<\/a><\/strong><\/li>\n<li>Cholera models with hyperinfectivity and temporary immunity (with J.H. Tien and P. van den Driessche).<br \/>\n<cite>Bulletin of Mathematical Biology,<\/cite> <b>74<\/b> (2012) 2423-2445. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/Cholera-models-2012bmb.pdf\">pdf<\/a><\/strong><\/li>\n<li>Reproduction numbers for infections with free-living pathogens growing in the environment (with M. Bani-Yaghoub, R. Gautam, P. van den Driessche, and R. Ivanek).<br \/>\n<cite>Journal of Biological Dynamics,<\/cite> <b>6<\/b> (2012) 923-940. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2012jbd.pdf\">pdf<\/a><\/strong><\/li>\n<li>Global dynamics of a general class of multi-stage models for infectious diseases (with H. Guo and M.Y. Li).<br \/>\n<cite>SIAM Journal on Applied Mathematics,<\/cite> <b>72<\/b> (2012) 261-279. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2012siap.pdf\">pdf<\/a><\/strong><\/li>\n<li>Impact of heterogeneity on the dynamics of an SEIR epidemic model (with P. van den Driessche).<br \/>\n<cite>Mathematical Biosciences and Engineering,<\/cite> <b>9<\/b> (2012) 393-411. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2012mbe.pdf\">pdf<\/a><\/strong><\/li>\n<li>Global dynamics of cholera models with differential infectivity (with P. van den Driessche).<br \/>\n<cite>Mathematical Biosciences,<\/cite> <b>234<\/b> (2011) 118-126. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2011mbs.pdf\">pdf<\/a><\/strong><\/li>\n<li>Global dynamics of a disease model including latency with distributed delays (with P. van den Driessche).<br \/>\n<cite>Canadian Applied Mathematics Quarterly,<\/cite> <b>19<\/b> (2011) 235-253. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2011camq.pdf\">pdf<\/a><\/strong><\/li>\n<li>Global-stability problem for coupled systems of differential equations on networks (with M.Y. Li).<br \/>\n<cite>Journal of Differential Equations,<\/cite> <b>248<\/b> (2010) 1-20. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2010jde.pdf\">pdf<\/a><\/strong><\/li>\n<li>Global stability of multi-group epidemic models with distributed delays (with M.Y. Li and C. Wang).<br \/>\n<cite>Journal of Mathematical Analysis and Applications,<\/cite> <b>361<\/b> (2010) 38-47. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2010jmaa.pdf\">pdf<\/a><\/strong><\/li>\n<li>Global stability of an epidemic model in a patchy environment (with M.Y. Li).<br \/>\n<cite>Canadian Applied Mathematics Quarterly,<\/cite> <b>17<\/b> (2009) 175-187. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2009camq.pdf\">pdf<\/a><\/strong><\/li>\n<li>A graph-theoretic approach to the method of global Lyapunov functions (with H. Guo and M.Y. Li).<br \/>\n<cite>Proceedings of the American Mathematical Society,<\/cite> <b>136<\/b> (2008) 2793-2802. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2008pams.pdf\">pdf<\/a><\/strong><\/li>\n<li>Optimization problems for general simple population with n-impulsive harvest (with L. Bai and K. Wang).<br \/>\n<cite>Journal of Mathematical Analysis and Applications,<\/cite> <b>329<\/b> (2007) 634-646. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2007jmaa.pdf\">pdf<\/a><\/strong><\/li>\n<li>Global stability of the endemic equilibrium of multigroup SIR epidemic models (with H. Guo and M.Y. Li).<br \/>\n<cite>Canadian Applied Mathematics Quarterly,<\/cite> <b>14<\/b> (2006) 259-284. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2006camq.pdf\">pdf<\/a><\/strong><\/li>\n<li>Optimal impulsive harvest policy for an autonomous system (with L. Bai and K. Wang).<br \/>\n<cite>Taiwanese Journal of Mathematics,<\/cite> <b>8<\/b> (2004) 245-258. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2004tjm.pdf\">pdf<\/a><\/strong><\/li>\n<li>Persistence and extinction of single population in a polluted environment (with Z. Li and K. Wang).<br \/>\n<cite>Electronic Journal of Differential Equations,<\/cite> 108 (2004) 1-5. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2004ejde.pdf\">pdf<\/a><\/strong><\/li>\n<li>Optimal impulsive harvesting policy for single population (with X. Zhang and K. Wang).<br \/>\n<cite>Nonlinear Analysis: Real World Applications,<\/cite> <b>4<\/b> (2003) 639-651. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2003narwa.pdf\">pdf<\/a><\/strong><\/li>\n<\/ul>\n<h2><strong>Funding Acknowledgement<\/strong><\/h2>\n<ul>\n<li>National Science Foundation<\/li>\n<li>Simons Foundation<\/li>\n<li>UCF Office of Research<\/li>\n<li>UCF College of Sciences<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Research Highlights A graph-theoretic approach to the construction of Lyapunov functions for large-scale differential equation systems references Target reproduction numbers with application to ecology and epidemiology references Mathematical modeling of waterborne diseases such as cholera Research team at UCF Erd\u00f6s number = 2 (Paul Erd\u0151s coauthored with John Moon, who is also my coauthor) Publications [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-17","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/pages\/17","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/comments?post=17"}],"version-history":[{"count":18,"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/pages\/17\/revisions"}],"predecessor-version":[{"id":301,"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/pages\/17\/revisions\/301"}],"wp:attachment":[{"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/media?parent=17"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}