{"id":{"repo_id":"vilnius","oai_identifier":"oai:vu.lt:elaba:81919505"},"canonical_url":"https://search.dev.ndltd.org/etd/vilnius/oai:vu.lt:elaba:81919505","repository":{"repo_id":"vilnius","name":"Vilnius University","base_url":"https://epublications.vu.lt/oai"},"display":{"title":"Tuberkuliozės matematinis modelis su netiesine gydymo funkcija /","abstract":"Mathematical model of tuberculosis with saturated treatment function. In this thesis SIR and SEIR tuberculosis models which include a saturated treatment function are studied. It is beneficial to include a saturated treatment in developing countries because medical conditions can be poor. The local and global stability of the equilibrium points determine the dynamics of the proposed models. Conditions for the global stability of the disease free equilibrium are given. It plays an important role in determining if an infection can be eradicated. The basic reproduction number $R_0$ is the average number of new infections generated by one infectious individual. While in most epidemiological models it is sufficient to decrease $R_0$ to below unity, in the SEIR model bistability may occur and different kinds of stable equilibria coexist. It is shown that improving medical conditions is an effective way of decreasing $R_0$ below a new threshold value $R_0^c$. An optimal control problem is then formulated to reduce the number of infected individuals. We illustrate the theoretical findings by using numerical simulations.","abstract_html":"Mathematical model of tuberculosis with saturated treatment function. In this thesis SIR and SEIR tuberculosis models which include a saturated treatment function are studied. It is beneficial to include a saturated treatment in developing countries because medical conditions can be poor. The local and global stability of the equilibrium points determine the dynamics of the proposed models. Conditions for the global stability of the disease free equilibrium are given. It plays an important role in determining if an infection can be eradicated. The basic reproduction number <span class=\"etd-inline-math\">R<sub>0</sub></span> is the average number of new infections generated by one infectious individual. While in most epidemiological models it is sufficient to decrease <span class=\"etd-inline-math\">R<sub>0</sub></span> to below unity, in the SEIR model bistability may occur and different kinds of stable equilibria coexist. It is shown that improving medical conditions is an effective way of decreasing <span class=\"etd-inline-math\">R<sub>0</sub></span> below a new threshold value <span class=\"etd-inline-math\">R<sub>0</sub><sup>c</sup></span>. An optimal control problem is then formulated to reduce the number of infected individuals. We illustrate the theoretical findings by using numerical simulations.","abstract_has_math":true,"creators":["Pranckūnas, Justinas,"],"institution":"Institutional Repository of Vilnius University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Štikonienė, Olga"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019","date_published":"2019","updated_at":"2026-07-24T05:55:48Z","subjects":[],"languages":["lit"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.vu.lt/VU:ELABAETD81919505&prefLang=en_US","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Štikonienė, Olga"]},{"key":"dc:creator","label":"Author","values":["Pranckūnas, Justinas,"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019"]},{"key":"dc:publisher","label":"Institution","values":["Institutional Repository of Vilnius University"]},{"key":"dc:relation","label":"Dc Relation","values":["https://epublications.vu.lt/object/elaba:81919505/81919505.pdf"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/bachelorThesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["lit"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://repository.vu.lt/VU:ELABAETD81919505&prefLang=en_US"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Mathematical model of tuberculosis with saturated treatment function. In this thesis SIR and SEIR tuberculosis models which include a saturated treatment function are studied. It is beneficial to include a saturated treatment in developing countries because medical conditions can be poor. The local and global stability of the equilibrium points determine the dynamics of the proposed models. Conditions for the global stability of the disease free equilibrium are given. It plays an important role in determining if an infection can be eradicated. The basic reproduction number $R_0$ is the average number of new infections generated by one infectious individual. While in most epidemiological models it is sufficient to decrease $R_0$ to below unity, in the SEIR model bistability may occur and different kinds of stable equilibria coexist. It is shown that improving medical conditions is an effective way of decreasing $R_0$ below a new threshold value $R_0^c$. An optimal control problem is then formulated to reduce the number of infected individuals. We illustrate the theoretical findings by using numerical simulations."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Tuberkuliozės matematinis modelis su netiesine gydymo funkcija /","Mathematical model of tuberculosis with saturated treatment function."]}]}],"canonical_facts":{"dc:contributor":["Štikonienė, Olga"],"dc:creator":["Pranckūnas, Justinas,"],"dc:date":["2019"],"dc:description":["Mathematical model of tuberculosis with saturated treatment function. In this thesis SIR and SEIR tuberculosis models which include a saturated treatment function are studied. It is beneficial to include a saturated treatment in developing countries because medical conditions can be poor. The local and global stability of the equilibrium points determine the dynamics of the proposed models. Conditions for the global stability of the disease free equilibrium are given. It plays an important role in determining if an infection can be eradicated. The basic reproduction number $R_0$ is the average number of new infections generated by one infectious individual. While in most epidemiological models it is sufficient to decrease $R_0$ to below unity, in the SEIR model bistability may occur and different kinds of stable equilibria coexist. It is shown that improving medical conditions is an effective way of decreasing $R_0$ below a new threshold value $R_0^c$. An optimal control problem is then formulated to reduce the number of infected individuals. We illustrate the theoretical findings by using numerical simulations."],"dc:format":["application/pdf"],"dc:identifier":["https://repository.vu.lt/VU:ELABAETD81919505&prefLang=en_US"],"dc:language":["lit"],"dc:publisher":["Institutional Repository of Vilnius University"],"dc:relation":["https://epublications.vu.lt/object/elaba:81919505/81919505.pdf"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:title":["Tuberkuliozės matematinis modelis su netiesine gydymo funkcija /","Mathematical model of tuberculosis with saturated treatment function."],"dc:type":["info:eu-repo/semantics/bachelorThesis"]},"updated_at":"2026-07-24T05:55:48Z"}