Tuberkuliozės matematinis modelis su netiesine gydymo funkcija /

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 R₀ is the average number of new infections generated by one infectious individual. While in most epidemiological models it is sufficient to decrease R₀ 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 R₀ below a new threshold value R₀^c. An optimal control problem is then formulated to reduce the number of infected individuals. We illustrate the theoretical findings by using numerical simulations.

Grantor dc:publisher

Institutional Repository of Vilnius University

Year dc:date

2019

Author dc:creator

• Pranckūnas, Justinas,

Contributors dc:contributor

• Štikonienė, Olga

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

lit

Repository record dc:identifier

https://repository.vu.lt/VU:ELABAETD81919505&prefLang=en_US

OAI identifier oai:identifier

oai:vu.lt:elaba:81919505