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Optimalno vodenje epidemije COVID-19 : magistrsko delo
ID Lampič, Jan (Author), ID Plestenjak, Bor (Mentor) More about this mentor... This link opens in a new window

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Abstract
Teorija sistemov upravljanja se je izkazala za uspešno orodje pri razumevanju različnih strategij obvladovanja nalezljivih bolezni. Teorija z iskanjem rešitve problema optimalnega vodenja, kontrole dinamičnega sistema, ki optimizira ciljni stroškovni funkcional, določa najboljšo strategijo izvajanja zajezitvenih ukrepov. Pri reševanju problema optimalnega vodenja za nepogrešljivega velja Pontrjaginov princip maksimuma. Princip predstavlja velik mejnik v teoriji sistemov upravljanja, saj neskončno dimenzionalni problem optimalnega vodenja pretvori v točkovno optimizacijo. V delu se na podlagi razširjenega SEIR modela, prilagojenega poteku bolezni COVID-19, oblikuje sistem upravljanja, ki vključuje kontrole za zmanjšanje prenosljivosti, testiranja in izolacije izpostavljenih, simptomatskih, asimptomatskih posameznikov ter večanja zmogljivosti zdravstvenega sistema. Z upoštevanjem razvitosti države se izpelje optimalne strategije izvajanja različnih kombinacij ukrepov. V primeru uporabe vseh ukrepov, rezultati kažejo, da bolj kot je država razvita, bolj intenzivno bi morala izvajati ukrepe za zmanjšanje prenosljivosti, večanja zdravstvenih kapacitet in testiranja simptomatsko okuženih posameznikov. Če pa država ni razvita in ni sposobna izvajati ukrepov, je najboljši pristop testiranje asimptomatskih posameznikov.

Language:Slovenian
Keywords:teorija sistemov upravljanja, optimalno vodenje, Pontrjaginov princip maksimuma, koronavirus, COVID-19
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FMF - Faculty of Mathematics and Physics
FRI - Faculty of Computer and Information Science
Year:2022
PID:20.500.12556/RUL-141962 This link opens in a new window
UDC:517.9
COBISS.SI-ID:125244163 This link opens in a new window
Publication date in RUL:13.10.2022
Views:943
Downloads:158
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Secondary language

Language:English
Title:Optimal control of the COVID-19 epidemic
Abstract:
Control theory has proven to be a successful tool in understanding ways to curtail the spread of infectious diseases. The theory determines the best strategy for implementing containment measures by finding a solution to the optimal control problem, which is a control of a dynamic system that optimizes the target cost functional. Pontryagin's maximum principle is considered indispensable when it comes to solving the problem of optimal control. The principle is regarded as a triumph of mathematical control theory since it transforms the infinite dimensional optimal control problem into a point optimization. Building on an extended SEIR model adapted to the COVID-19 disease a control system incorporating various possible interventions is formulated. The system models interventions which include transmission reduction, testing and isolation of the exposed, symptomatic, asymptomatic individuals and increasing healthcare capacity. Optimal strategies for the implementation of various interventions are derived by considering the country's capacity. Results show that, if all the controls are to be used, the more able the country is, the more it should implement measures to reduce transmission, increase health capacities and test symptomatically infected individuals. However, if the country finds it very difficult to implement the controls, the best approach is to test asymptomatic individuals.

Keywords:control theory, optimal control, Pontryagin's maximum principle, coronavirus, COVID-19

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