{"id":4941,"date":"2025-06-24T11:33:30","date_gmt":"2025-06-24T11:33:30","guid":{"rendered":"https:\/\/fs.kibu.ac.ke\/?p=4941"},"modified":"2025-12-26T23:37:20","modified_gmt":"2025-12-26T23:37:20","slug":"mathematical-modelling-and-optimal-controls-for-controlling-pneumonia-hiv-co-infection","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/fs\/mathematical-modelling-and-optimal-controls-for-controlling-pneumonia-hiv-co-infection\/","title":{"rendered":"Mathematical Modelling and Optimal Controls for Controlling Pneumonia-HIV Co-Infection"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"4941\" class=\"elementor elementor-4941\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-54d3f62f elementor-section-full_width elementor-section-height-min-height elementor-section-items-stretch elementor-section-height-default\" data-id=\"54d3f62f\" 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-5f8148bd\" data-id=\"5f8148bd\" 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-21912f0 elementor-widget elementor-widget-theme-post-title elementor-page-title elementor-widget-heading\" data-id=\"21912f0\" data-element_type=\"widget\" data-widget_type=\"theme-post-title.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Mathematical Modelling and Optimal Controls for Controlling Pneumonia-HIV Co-Infection<\/h1>\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-2e149fad elementor-section-height-min-height elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"2e149fad\" 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-27222659\" data-id=\"27222659\" 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-75e19eb7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"75e19eb7\" 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-5822beda elementor-invisible\" data-id=\"5822beda\" 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-2516b192 elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"2516b192\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">2021<\/h2>\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-60d4ec8b elementor-invisible\" data-id=\"60d4ec8b\" 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-18e21f78 elementor-widget elementor-widget-heading\" data-id=\"18e21f78\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">KIBU Authors<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3cf31454 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"3cf31454\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Nebert Kituni Wafula<\/p><p>Boniface Otieno Kwach<\/p><p>Vincent Nyongesa Marani<\/p>\t\t\t\t\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-e7e17da elementor-invisible\" data-id=\"e7e17da\" 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-612ed9de elementor-tablet-align-left elementor-invisible elementor-widget elementor-widget-button\" data-id=\"612ed9de\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInLeft&quot;}\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-shrink\" href=\"https:\/\/www.internationaljournalcorner.com\/index.php\/ijird_ojs\/article\/view\/158134\/109238\">\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\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-inner-section elementor-element elementor-element-1ce4c2fb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1ce4c2fb\" 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-100 elementor-inner-column elementor-element elementor-element-1b0ef283 elementor-invisible\" data-id=\"1b0ef283\" 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-77225115 elementor-widget elementor-widget-heading\" data-id=\"77225115\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\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 class=\"elementor-element elementor-element-6c3eb28b elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"6c3eb28b\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Bacterial infections like Pneumonia have emerged as an important cause of morbidity and mortality in individuals infected with HIV giving rise to their co-infection. There are mathematical models that describe; the co-dynamics, treatment and protection mechanisms of Pneumonia and HIV infections. Therefore, this research is aimed at determining optimal control treatments through developing a deterministic mathematical model Pneumonia-HIV co-infection incorporating the use of anti-pneumonia and ART treatment interventions as controls. The uncontrolled pneumonia-HIV co-infection is presented with its analysis. Finally, the optimal control theory for Pneumonia-HIV co-infection model is derived analytically by applying the Pontryagin&#8217;s Maximum Principle.<\/p>\t\t\t\t\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\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>2021 KIBU Authors Nebert Kituni Wafula Boniface Otieno Kwach Vincent Nyongesa Marani VIEW ON PUBLISHER SITE Abstract Bacterial infections like Pneumonia have emerged as an important cause of morbidity and mortality in individuals infected with HIV giving rise to their co-infection. There are mathematical models that describe; the co-dynamics, treatment and protection mechanisms of Pneumonia [&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":[9],"tags":[],"class_list":["post-4941","post","type-post","status-publish","format-standard","hentry","category-research-list"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Mathematical Modelling and Optimal Controls for Controlling Pneumonia-HIV Co-Infection - Faculty of Science<\/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\/fs\/mathematical-modelling-and-optimal-controls-for-controlling-pneumonia-hiv-co-infection\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mathematical Modelling and Optimal Controls for Controlling Pneumonia-HIV Co-Infection - Faculty of Science\" \/>\n<meta property=\"og:description\" content=\"2021 KIBU Authors Nebert Kituni Wafula Boniface Otieno Kwach Vincent Nyongesa Marani VIEW ON PUBLISHER SITE Abstract Bacterial infections like Pneumonia have emerged as an important cause of morbidity and mortality in individuals infected with HIV giving rise to their co-infection. There are mathematical models that describe; the co-dynamics, treatment and protection mechanisms of Pneumonia [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/kibu.ac.ke\/fs\/mathematical-modelling-and-optimal-controls-for-controlling-pneumonia-hiv-co-infection\/\" \/>\n<meta property=\"og:site_name\" content=\"Faculty of Science\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-24T11:33:30+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-26T23:37:20+00:00\" \/>\n<meta name=\"author\" content=\"kibabii\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"kibabii\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/mathematical-modelling-and-optimal-controls-for-controlling-pneumonia-hiv-co-infection\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/mathematical-modelling-and-optimal-controls-for-controlling-pneumonia-hiv-co-infection\/\"},\"author\":{\"name\":\"kibabii\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/#\/schema\/person\/fc9b7f13eeb65cf0be520197c35b17d6\"},\"headline\":\"Mathematical Modelling and Optimal Controls for Controlling Pneumonia-HIV Co-Infection\",\"datePublished\":\"2025-06-24T11:33:30+00:00\",\"dateModified\":\"2025-12-26T23:37:20+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/mathematical-modelling-and-optimal-controls-for-controlling-pneumonia-hiv-co-infection\/\"},\"wordCount\":123,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/#organization\"},\"articleSection\":[\"Research List\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/kibu.ac.ke\/fs\/mathematical-modelling-and-optimal-controls-for-controlling-pneumonia-hiv-co-infection\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/mathematical-modelling-and-optimal-controls-for-controlling-pneumonia-hiv-co-infection\/\",\"url\":\"https:\/\/kibu.ac.ke\/fs\/mathematical-modelling-and-optimal-controls-for-controlling-pneumonia-hiv-co-infection\/\",\"name\":\"Mathematical Modelling and Optimal Controls for Controlling Pneumonia-HIV Co-Infection - 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