Matematisk modellering af mæslinger: Mathematical modelling of measles

Christoffer Dalgaard, Lasse Sønderskov Hansen, Natasja Nielsen, Rasmus Kristoffer Pedersen, Jeanette Rasmussen & Michael Fouchard Sylvest-Nielsen

Studenteropgave: Semesterprojekt

Abstrakt

Abstract: In this report a mathematical model of the dynamics of measles is developed. The goal of this report is to modify a mathematical model in such a way that it is possible to model age shift and to find the rate of vaccination necessary for extermination of measles in Denmark. The model has been created on basis of an SEIR model divided into 100 age steps. Through results from the model, line charts depicting number of cases of disease per year, age distribution, and cases of disease as a function of the rate of vaccination. From these charts it has been concluded that the model is capable of showing age shift of the cases of disease as an effect of vaccination. The age shift causes the number of cases of disease for people older than 18 years of age will increase as an effect of vaccination if the rate of vaccination does not surpass 82.4%. Additionally it is observed that with a rate of vaccination of 50% an ageshift is found which corresponds to the ageshift found by Panagiotopoulos et al. (1999). Furthermore it is concluded that the rate of vaccination in Denmark is over the limit required to ensure a decrease in the number of cases of disease for people older than 18 years of age, but too low to exterminate measles as this critical rate of vaccination is found to be between 87% and 88%. Resumé I denne rapport opstilles en matematisk model for mæslingers dynamik i en befolkning. Målet med rapporten var at modificere en matematisk model således, at denne kunne modellere aldersforskydning og bruges til at finde vaccinationsraten nødvendig for at udrydde mæslinger i Danmark. Modellen blev opbygget over en aldersinddelt SEIR model, og indeholder 100 alderstrin. Ved hjælp af modellens resultater blev der udformet grafer for antallet af sygdomstilfælde per år, aldersfordeling og smittetilfælde som funktion af vaccinationsraten. Ud fra disse grafer er det blevet konkluderet at modelen er i stand til at påvise en aldersforskydning af de smittede som følge af vaccination. Denne aldersforskydning medfører at mængden af smittede over 18 år vil stige som følge af vaccination hvis vaccinationsraten ligger under 82,4%. Derudover er der ved en vaccinationsprocent på 50% blevet observeret en aldersforskydning der stemmer overens med den der har fundet sted i Panagiotopoulos et al. (1999). Ydermere konkluderes det at vaccinationsraten i Danmark er høj nok til at medføre et fald i antallet af smittede over 18 år, men for lav til at udrydde mæslinger, da denne kritisk vaccinationsrate er fundet til at ligge mellem 87% og 88%.

UddannelserMatematik, (Bachelor/kandidatuddannelse) Bachelor el. kandidat
SprogDansk
Udgivelsesdato17 jan. 2014
VejledereViggo Andreasen

Emneord

  • matematisk
  • modellering
  • mæslinger
  • modelling
  • measles
  • matematical