# Johan Klint: Simulating carriage of an infectious disease using mathematical models

**Time: **
Wed 2019-12-11 09.00 - 10.00

**Lecturer: **
Johan Klint

**Location: ** Kräftriket, house 5, room 32

### Abstract

Mathematical models serve as a means of studying the spread of infectious diseases in populations, and to estimate the expected benefit of an intervention, often the introduction of a vaccination program on a national level. The simulated results depend not only on the input parameters, but also on structural model assumptions. These assumptions may be demographic, e.g. related to births, aging and death, or epidemiologic, e.g. dynamic or static force of infection or the competitive interaction between related infectious agents. The choices made when creating such models affect the decision whether or not a national vaccination program will be implemented.

In this study we investigate the spread of the infectious bacterium Neisseria meningitidis in a human population. We intend to develop a comprehensive model with the attempt to realistically simulate the disease spread on a national level. However, for mathematical tractability model simplifications are a necessity. We therefore perform some mathematical analysis on simplified models to find explicit solutions and determine stability of equilibria.

A comprehensive disease transmission model was created considering both demography and age-related epidemiology. By incorporating such features, we obtain models intended to be realistic with the ability to simulate a country’s demographic development over time, as well as age-dependent properties of disease transmission. The developed model was first implemented for one bacterial strain with corresponding vaccine. Results were obtained comparing dynamic versus static force of infection (FOI), where the static FOI underestimated the impact of a vaccine intervention as expected. The model was further extended with an additional competing bacterial strain. The strain replacement effect was observed, and a condition allowing for co-existence of competing strains was found by using nullcline analysis.