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.
Highlights
The first objective of this paper is to analyse the non-specific effects of a vaccination with the Bacille Calmette-Guerin (BCG) vaccine for limitations of other diseases
The main problem is to generate an output in which the four parameter values lie in the intervals of Table 1. Since this is realised in only a few cases, the search for a minimum error for certain m and n is performed until parameter values meet special conditions
Based on the data set on pro-rata pneumonia symptoms of the population we examine stochastic dependence on BCG vaccination quotas
Summary
The first objective of this paper is to analyse the non-specific effects of a vaccination with the Bacille Calmette-Guerin (BCG) vaccine for limitations of other diseases. The second objective is a determination of conditions and parameters for a model-specific forecast concerning prevalence of tuberculosis afflictions, as well as an evaluation of the used mathematical model. The relevance of the associated elaborations arises from the current increase in the incidence rate of tuberculosis infection in Germany, which is accounted for by cross-border refugee movements, high rates of infection in at-risk groups. Identifications of an outbreak of tuberculosis often need a considerable amount of time because hardly any specialised centres exist due to the rare occurrence of this disease over several decades. In Germany, where the number of infections is rather low compared to other countries, tuberculosis is a rather rarely addressed taboo subject. Very high rates of infection are registered in Eastern Europe, where a rise in antibiotic resistances is detected [57]
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