{"id":22,"date":"2012-09-05T11:22:33","date_gmt":"2012-09-05T15:22:33","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/template\/?page_id=22"},"modified":"2026-03-19T08:16:30","modified_gmt":"2026-03-19T12:16:30","slug":"research","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/maia\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Research<\/h1>\n\n\n\n<p>I am a mathematical biologist interested in modeling biological phenomena. I use population dynamics approach to modeling. Basic mathematical tools that I use include<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Ordinary differential equations<\/li>\n<li>Age-structured partial differential equations<\/li>\n<li>Discrete delay and distributed delay differential equations<\/li>\n<li>Discrete equations<\/li>\n<li>Diffusion equations<\/li><\/ul>\n\n\n\n<p>All models that I consider are deterministic models. I am interested in studying equilibria and their local and global stability. I have found chaos in some of my models. I also devise\u00a0 numerical methods for the partial differential equation models. In addition, I am interested in fitting models to data and performing model selection.<\/p>\n\n\n\n\n\n<p>Biological themes that I have been investigating are:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Epidemiology of infectious diseases: avian influenza, malaria, HIV<\/li>\n<li>Immunology of infectious diseases: Hepatitis C, WNV, HIV, M. Paratuberculosis (MAP)<\/li>\n<li>Linking immunological and epidemiological modeling of infectious diseases<\/li>\n<li>Meta-population modeling<\/li>\n<li>Predator-prey and competition modeling<\/li>\n<li>Erythropoesis in dialysis patients<\/li>\n<li>HIV and opioids<\/li><\/ul>\n\n\n\n\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":310,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-22","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/maia\/wp-json\/wp\/v2\/pages\/22","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/maia\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/maia\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/maia\/wp-json\/wp\/v2\/users\/310"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/maia\/wp-json\/wp\/v2\/comments?post=22"}],"version-history":[{"count":6,"href":"https:\/\/people.clas.ufl.edu\/maia\/wp-json\/wp\/v2\/pages\/22\/revisions"}],"predecessor-version":[{"id":1032,"href":"https:\/\/people.clas.ufl.edu\/maia\/wp-json\/wp\/v2\/pages\/22\/revisions\/1032"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/maia\/wp-json\/wp\/v2\/media?parent=22"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}