Mathematical model for cancer prevalence and cancer mortality

J 2013

Mathematical model for cancer prevalence and cancer mortality

KALAS, Josef; Jan NOVOTNÝ; Jaroslav MICHÁLEK a Oleksandr NAKONECHNY

Základní údaje

Originální název

Mathematical model for cancer prevalence and cancer mortality

Název česky

Matematický model šíření rakoviny a úmrtnosti na rakovinu

Autoři

KALAS, Josef; Jan NOVOTNÝ; Jaroslav MICHÁLEK a Oleksandr NAKONECHNY

Vydání

Taurida Journal of Computer Science Theory and Mathematics, Simferopol, Crimean Scientific Center of National Academy of Sciences, Taurida National V. I. Vernadsky University, 2013, 1729-3901

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Ukrajina

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/13:00066928

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Deterministic model; differential equations; asymptotic properties; cancer prevalence and mortality in a population; short-term prediction; long-term prediction; regression model.

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 13. 3. 2018 13:39, doc. RNDr. Josef Kalas, CSc.

Anotace

V originále

The first part of the paper designs a deterministic model to describe cancer prevalence and mortality in a population. Next the asymptotic properties of the model are investigated. In the second part, the model is applied to real-world data. For selected model data, a numerical solution is found to the differential equations describing the model, a long-term prediction is made with its results compared with those of predictions made by regression analysis, which are often used to model the prevalence and mortality in the present literature. It is shown that, although for short-term predictions (up to 10 years) both approaches are nearly equivalent, there is a major difference between them if a longer-term prediction is made and finding a reliable prediction for a period longer than 10 years based on short time series seems to be unlikely.

Návaznosti

GA201/08/0469, projekt VaV

Název: Oscilační a asymptotické vlastnosti řešení diferenciálních rovnic

Investor: Grantová agentura ČR, Oscilační a asymptotické vlastnosti řešení diferenciálních rovnic

Citovat

KALAS, Josef; Jan NOVOTNÝ; Jaroslav MICHÁLEK a Oleksandr NAKONECHNY. Mathematical model for cancer prevalence and cancer mortality. Taurida Journal of Computer Science Theory and Mathematics. Simferopol: Crimean Scientific Center of National Academy of Sciences, Taurida National V. I. Vernadsky University, 2013, roč. 2013, č. 2, s. 44-54. ISSN 1729-3901.

@article{1166341,
   author = {Kalas, Josef and Novotný, Jan and Michálek, Jaroslav and Nakonechny, Oleksandr},
   article_location = {Simferopol},
   article_number = {2},
   keywords = {Deterministic model; differential equations; asymptotic properties; cancer prevalence and mortality in a population; short-term prediction; long-term prediction; regression model.},
   language = {eng},
   issn = {1729-3901},
   journal = {Taurida Journal of Computer Science Theory and Mathematics},
   title = {Mathematical model for cancer prevalence and cancer mortality},
   url = {http://tvim.info/files/tvim_2013_2.pdf},
   volume = {2013},
   year = {2013}
}

TY  - JOUR
ID  - 1166341
AU  - Kalas, Josef - Novotný, Jan - Michálek, Jaroslav - Nakonechny, Oleksandr
PY  - 2013
TI  - Mathematical model for cancer prevalence and cancer mortality
JF  - Taurida Journal of Computer Science Theory and Mathematics
VL  - 2013
IS  - 2
SP  - 44-54
EP  - 44-54
PB  - Crimean Scientific Center of National Academy of Sciences, Taurida National V. I. Vernadsky University
SN  - 17293901
KW  - Deterministic model
KW  - differential equations
KW  - asymptotic properties
KW  - cancer prevalence and mortality in a population
KW  - short-term prediction
KW  - long-term prediction
KW  - regression model.
UR  - http://tvim.info/files/tvim_2013_2.pdf
L2  - http://tvim.info/files/tvim_2013_2.pdf
N2  - The first part of the paper designs a deterministic model to describe cancer prevalence and mortality in a population. Next the asymptotic properties of the model are investigated. In the second part, the model is applied to real-world data. For selected model data, a numerical solution is found to the differential equations describing the model, a long-term prediction is made with its results compared with those of predictions made by regression analysis, which are often used to model the prevalence and mortality in the present literature. It is shown that, although for short-term predictions (up to 10 years) both approaches are nearly equivalent, there is a major difference between them if a longer-term prediction is made and finding a reliable prediction for a period longer than 10 years based on short time series seems to be unlikely.
ER  -

KALAS, Josef; Jan NOVOTNÝ; Jaroslav MICHÁLEK a Oleksandr NAKONECHNY. Mathematical model for cancer prevalence and cancer mortality. \textit{Taurida Journal of Computer Science Theory and Mathematics}. Simferopol: Crimean Scientific Center of National Academy of Sciences, Taurida National V. I. Vernadsky University, 2013, roč.~2013, č.~2, s.~44-54. ISSN~1729-3901.

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