Nahirniak, V.M.

Цифровий Репозиторій - Інтелектуальні Фонди Буковинського державного медичного університету

459Nahirniak V.M.THE USE OF CURVE-FITTING IN MATLAB FOR FINDING THE MAINPARAMETERS OF THE COMPARTMENT MODEL OF EPIDEMICSDepartment of Biological Physics and Medical InformaticsBukovinian State Medical UniversityCompartmental models are used to predict a worldwide spread of infection and declarationof a pandemic. For such cases, researchers use the SIR model.  It was used when the outbreak ofEbola virus had happened. It started in Guinea and then spread across land borders to Sierra Leoneand Liberia. The epidemiology data were analyzed, and processed using the SIR model.The SIR compartmental model is based on three linear differential equations with two mainparameters β (t) and γ (t) for three chambers or categories of people:where S (t) - susceptible to infection people, I (t) – infected ones, R (t) – recovered ones.Modeling the dynamics of infectious diseases requires to determine whether the spread ofthe disease can reach epidemic levels or can be gradually eradicated. According to the SIR model,the slowdown in epidemics occurred after the number of infected people reaches its peak. Thetheoretical model of SIR allows predicting the results of epidemics and the factors that determine itsseverity.The physical meaning of β (t) is the number of contacts during which the infection getstransmitted per person per unit time. By reducing the coefficient β by various anti-epidemiologicalmeasures, we can reduce the rate of spread of infectionThe physical meaning of γ (t) is the share of infected people who have recovered per unittime. It demonstrates how effective the treatment of the infected is.The development and course of the epidemic depends on these two factors. From theequations it is seen that in the case when βS (t) <γ, then dI / dt <0 and the epidemic dies off on itsown. If βS (t)> γ, then dI / dt> 0 and the number of the infected people increases dramatically. Thisleads to a rapid spread of the epidemic. Thus, the way to limit the epidemic may includeimmunization, which leads to a decrease in the number of susceptible to infection S (t), or adecrease in the coefficient β (t), i.e. the rate of transmission from one person to another. The lattercan be achieved through quarantine, lockdown, promotion of disinfection culture.The values of the parameters β (t) and γ (t) can be determined on the basis of statistical dataobtained for three categories of people. The collected data are stochastic in nature and arecharacterized by strong variability. To more accurately determine the parameters of the chambermodel, we used the utility Curve Fitting software environment MATLAB (Mathworks, MA, USA)to determine the analytical function that describes this data set. Having determined the analyticalfunction that most accurately describes the statistics, it is possible to estimate the values ofparameters β(t) and γ (t) during a certain period of the epidemic. For example at the beginning ofquarantine and accordingly at the end of it. This analysis allows us assessing the effectiveness ofanti-epidemiological measures.Olar O.I.NANOTECHNOLOGIES - HEALTH HAZARDSDepartment of Biological Physics and Medical InformaticsBukovinian State Medical UniversityIdentification and unification of the properties of most nanomaterials (NMs) clearly outlinedthe area of their application. Exceptional properties of nanoparticles (NPs) have become the drivingforce of their widespread use in the biomedical field. High photostability, significant quantum yieldand absorption coefficient in a wide spectral range allowed to obtain molecular imaging (e.g., NPcan be used as probesin vivo by their attach to molecules of proteins, antibodies and nucleic acids;NP can be used as an instrument of evaluation of molecular reactions in the body, etc.).

The use of curve-fitting in matlab for finding the main parameters of the compartment model of epidemic

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The use of curve-fitting in matlab for finding the main parameters of the compartment model of epidemic

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Цифровий Репозиторій - Інтелектуальні Фонди Буковинського державного медичного університету