{"id":9671,"date":"2025-12-09T11:07:39","date_gmt":"2025-12-09T11:07:39","guid":{"rendered":"https:\/\/kibu.ac.ke\/sgs\/?p=9671"},"modified":"2025-12-09T11:10:05","modified_gmt":"2025-12-09T11:10:05","slug":"theoretical-properties-of-an-adaptive-spatial-hierarchical-bayesian-seir-model-for-hiv-transmission-dynamics","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/sgs\/theoretical-properties-of-an-adaptive-spatial-hierarchical-bayesian-seir-model-for-hiv-transmission-dynamics\/","title":{"rendered":"Theoretical Properties of an Adaptive Spatial Hierarchical Bayesian SEIR Model for HIV Transmission Dynamics"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"9671\" class=\"elementor elementor-9671\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-24e97885 elementor-section-full_width elementor-section-height-min-height elementor-section-items-stretch elementor-section-height-default\" data-id=\"24e97885\" data-element_type=\"section\" id=\"ourgoal\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-349db574\" data-id=\"349db574\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aae8305 elementor-widget elementor-widget-theme-post-title elementor-page-title elementor-widget-heading\" data-id=\"aae8305\" data-element_type=\"widget\" data-widget_type=\"theme-post-title.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Theoretical Properties of an Adaptive Spatial Hierarchical Bayesian SEIR Model for HIV Transmission Dynamics<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2af12871 elementor-section-height-min-height elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"2af12871\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7a74869\" data-id=\"7a74869\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-1fb4b804 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1fb4b804\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-4cf1d18b elementor-invisible\" data-id=\"4cf1d18b\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-82ee43f elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"82ee43f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">2025<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1f46ddd5 elementor-invisible\" data-id=\"1f46ddd5\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3e7823d6 elementor-widget elementor-widget-heading\" data-id=\"3e7823d6\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Authors<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-78ff75ec elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"78ff75ec\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Mulati Omukoba Nyukuri<\/p><p>John Sirengo<\/p><p>Lucy Chikamai<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-343f60d8 elementor-invisible\" data-id=\"343f60d8\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4b001ed3 elementor-tablet-align-left elementor-invisible elementor-widget elementor-widget-button\" data-id=\"4b001ed3\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInLeft&quot;}\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-shrink\" href=\"https:\/\/www.irejournals.com\/paper-details\/1709801\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">VIEW ON PUBLISHER SITE<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-79f85a3e elementor-widget elementor-widget-heading\" data-id=\"79f85a3e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-875e86 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"875e86\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>This study establishes theoretical foundations of an adaptive spatial hierarchical Bayesian SEIR model for HIV transmission dynamics. We prove existence and uniqueness of solutions, derive equilibrium conditions, analyze stability properties, and establish convergence guarantees. The enhanced SEIR model incorporates spatial heterogeneity through time-varying connectivity weights and employs hierarchical Bayesian methods for robust parameter estimation. Key results include global existence of nonnegative solutions, stability conditions for disease-free equilibrium, derivation of spatial basic reproduction number R\u2080 = \u03c1(FV\u207b\u00b9), and geometric ergodicity of MCMC estimation. Stability analysis demonstrates global asymptotic stability when R\u2080 \u2264 1. These theoretical properties provide rigorous mathematical foundations for HIV control strategies in resource-limited settings.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>2025 Authors Mulati Omukoba Nyukuri John Sirengo Lucy Chikamai VIEW ON PUBLISHER SITE Abstract This study establishes theoretical foundations of an adaptive spatial hierarchical Bayesian SEIR model for HIV transmission dynamics. We prove existence and uniqueness of solutions, derive equilibrium conditions, analyze stability properties, and establish convergence guarantees. The enhanced SEIR model incorporates spatial heterogeneity [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-9671","post","type-post","status-publish","format-standard","hentry","category-publications"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Theoretical Properties of an Adaptive Spatial Hierarchical Bayesian SEIR Model for HIV Transmission Dynamics - School of Graduate Studies<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/kibu.ac.ke\/sgs\/theoretical-properties-of-an-adaptive-spatial-hierarchical-bayesian-seir-model-for-hiv-transmission-dynamics\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Theoretical Properties of an Adaptive Spatial Hierarchical Bayesian SEIR Model for HIV Transmission Dynamics - School of Graduate Studies\" \/>\n<meta property=\"og:description\" content=\"2025 Authors Mulati Omukoba Nyukuri John Sirengo Lucy Chikamai VIEW ON PUBLISHER SITE Abstract This study establishes theoretical foundations of an adaptive spatial hierarchical Bayesian SEIR model for HIV transmission dynamics. We prove existence and uniqueness of solutions, derive equilibrium conditions, analyze stability properties, and establish convergence guarantees. 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We prove existence and uniqueness of solutions, derive equilibrium conditions, analyze stability properties, and establish convergence guarantees. 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