elektronický časopis
- MeSH
- Immune Tolerance MeSH
- Immunologic Deficiency Syndromes MeSH
- Models, Theoretical MeSH
- Publication type
- Review MeSH
Práca sa zaoberá významom matematického modelovania v epidemiológii. Rozoberá princípy deterministického modelu SIR (vnímavý – infekčný – imúnny), ktorý sa používa predovšetkým na popis šírenia ochorení detského veku a predstavuje koncept kolektívnej imunity v súvislosti so základným reprodukčným číslom a očkovaním. Na príklade otvoreného SIR modelu podávame vysvetlenie základných čŕt šírenia ochorení zanechávajúcich trvalú imunitu ako sú morbilli, parotitída, varicella a rubeola. Vývoj proporcie vnímavých, infekčných a imúnnych má v nezaočkovanej populácii charakter tlmených oscilácií. Výkyvy v proporciách jednotlivých skupín sú navzájom prepojené. Vplyvom pôrodnosti sa hromadí počet vnímavých až na kritickú hodnotu, kedy dôjde k „vzplanutiu“ epidémie, k zvýšeniu proporcie infekčných. To má za následok prudké znižovanie proporcie vnímavých, čo však zároveň brzdí šírenie ochorenia. Očkovanie zásadným spôsobom ovplyvňuje výskyt ochorení. Ak je zaočkovanosť nižšia ako hodnota hranice kolektívnej imunity, dochádza k obmedzeniu šírenia ochorenia. Priemerné hodnoty proporcie vnímavých sa zásadným spôsobom nemenia. Ak dôjde vplyvom očkovania k prekročeniu hranice kolektívnej imunity, podľa modelu sa ochorenie prestáva šíriť, proporcia vnímavých postupne klesá. Na Slovensku sa zo spomínaných ochorení plošne očkuje proti morbillám, rubeole a parotitíde. Situácia vo výskyte týchto ochorení je momentálne priaznivá a okrem menších lokálnych epidémií parotitídy sa tieto ochorenia v posledných rokoch na Slovensku už nevyskytujú. Napriek tomu je nevyhnutné brať do úvahy možné zmeny epidemiologickej situácie najmä vzhľadom na nárast antivakcinačných aktivít. Lebo ako je aj z našej práce zrejmé, nahromadenie vnímavých nad určitú hranicu predstavuje riziko z hľadiska znovuvznietenia epidémii.
The article deals with mathematical modeling in epidemiology and analyses principles of deterministic SIR model (susceptible – infected – resistant) which is used particularly to describe spread of infectious childhood diseases and represents a concept of herd immunity in association with a basic reproduction number and vaccination. Using the open SIR model, we can explain basic features of spread of diseases causing permanent immunity such as mumps, varicella, measles and rubella. Development of proportions of susceptible, infected and resistant individuals in non-vaccinated population shows a character of damped oscillations. Oscillations of proportions of individual groups are mutually interconnected. As an effect of a birth rate, the number of susceptible individuals increases up to a critical level, when the epidemic outbreak emerges followed by increase of proportion of infected individuals. This leads to a dramatic decrease of proportion of susceptible individuals resulting in deceleration of spread of the infection. The vaccination substantially influences occurrence of the disease. If the vaccination rate is below of a threshold of the herd immunity, spread of infection is limited. However, mean values of proportions of susceptible individuals are not significantly changed. If the vaccination rate exceeds the level needed for the herd immunity, according to the model, spread of the infection is halted and the proportion of susceptible persons continuously decreases. In Slovakia, within the above mentioned diseases, mass vaccination against measles, rubella and mumps is provided. Situation regarding occurrence of these disease is relatively favorable and except minor local outbreaks of mumps they almost do not occur in Slovakia. However, we should take into account possible changes of epidemiological situation, particularly considering increase of antivaccination activities. As seen in our contribution, accumulation of susceptible individuals above certain level constitutes a risk of reemerging of epidemic outbreaks.
- Keywords
- matematické modelování,
- MeSH
- Child MeSH
- Immunity, Herd * MeSH
- Humans MeSH
- Numerical Analysis, Computer-Assisted MeSH
- Parotitis immunology prevention & control MeSH
- Chickenpox immunology prevention & control MeSH
- Computer Simulation MeSH
- Child, Preschool MeSH
- Measles immunology prevention & control MeSH
- Models, Theoretical * MeSH
- Vaccination * MeSH
- Rubella immunology prevention & control MeSH
- Check Tag
- Child MeSH
- Humans MeSH
- Child, Preschool MeSH
- Publication type
- Research Support, Non-U.S. Gov't MeSH
- MeSH
- Myocardial Contraction MeSH
- Muscle Contraction MeSH
- Models, Theoretical MeSH
- Publication type
- Review MeSH
This work answers some questions related to detection of rheological properties of soft tissues exemplified in myometrium, stressed by external tensile force. In the first stage of the experiment the tissue samples were ciclically stressed and response loops were recorded. This test proved severe plastical deformation of samples, which is not usually being stated for living tissues. In addition to course, growth and stabilizing this deformation also energetical losses of individual hysteresis loops of the response were evaluated. In the second stage of the experiment the tissue samples were exposed to a loading force changed in step-wise manner in four steps. The sample response to each force step was processed and evaluated separately to obtain basic properties of used model. In next step, the changes in model characteristics were obtained and evaluated for each element in subsequent force steps. By reason of following easier interpretation, the quite simple visco-elastic model, defined by differential equation with analytic solution, is used. The results prove necessary to introduce in model both spring and damper constants dependent on the magnitude of the loading force and one damper with even time dependent constant. The interindividual variability of characteristic values of the model elements is surprisingly low. On the other side, they are strongly dependent on load magnitude. Complete mathematical model of uterine wall tissue is obtained by amending the principal equation by formulas describing changes in individual components of the model.
