Compartment models for vaccine effectiveness and non-specific effects for Tuberculosis

Sarah Treibert; Helmut Brunner; Matthias Ehrhardt; Sarah Treibert; Helmut Brunner; Matthias Ehrhardt

doi:10.3934/mbe.2019364

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 7250-7298. doi: 10.3934/mbe.2019364

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Research article

Compartment models for vaccine effectiveness and non-specific effects for Tuberculosis

1.
Albert-Ludwigs-Universität Freiburg, Ernst-Zermelo Strasse 1, 79104 Freiburg, Germany
2.
Medizinische Fakultät, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany
3.
Center for Health Economics and Health Services Research, Bergische Universität Wuppertal, Gaussstrasse 20, 42119 Wuppertal, Germany
4.
Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Bergische Universität Wuppertal, Gaussstrasse 20, 42119 Wuppertal, Germany

Received: 12 September 2018 Accepted: 10 June 2019 Published: 09 August 2019

In this paper, we attempt to set a framework of conditions for model-specific predictions of newly arising TB epidemics by e.g. immigration of infected persons from high prevalence countries. In addition, we address the aspect of trained immunity in our model. Using a mathematical approach of a system of ordinary differential equations which can be developed over several time-points we obtained varying infection or attack rates that led to different effects of the vaccination, depending on the setting of certain parameters and starting values in the compartments of a SEIR-model. We finally obtained different graphs of disease progression and were able to outline which upgrades and expansions our system requires in order to be exact and well adapted for predicting the course of future TB outbreaks. The model might also be beneficial in predicting non-specific effects of vaccines.
- compartment models,
- SEIR model,
- ODE system,
- Tuberculosis,
- trained Immunity,
- vaccination,
- non-specific effects
Citation: Sarah Treibert, Helmut Brunner, Matthias Ehrhardt. Compartment models for vaccine effectiveness and non-specific effects for Tuberculosis[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7250-7298. doi: 10.3934/mbe.2019364

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Abstract

In this paper, we attempt to set a framework of conditions for model-specific predictions of newly arising TB epidemics by e.g. immigration of infected persons from high prevalence countries. In addition, we address the aspect of trained immunity in our model. Using a mathematical approach of a system of ordinary differential equations which can be developed over several time-points we obtained varying infection or attack rates that led to different effects of the vaccination, depending on the setting of certain parameters and starting values in the compartments of a SEIR-model. We finally obtained different graphs of disease progression and were able to outline which upgrades and expansions our system requires in order to be exact and well adapted for predicting the course of future TB outbreaks. The model might also be beneficial in predicting non-specific effects of vaccines.

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