Abstract
A common modelling approach in public health and epidemiology divides the population under study into compartments containing persons that share the same status. Here we consider a three-state model with the compartments: A, B and Dead. States A and B may be the states of any dichotomous variable, for example, Healthy and Ill, respectively. The transitions between the states are described by change rates, which depend on calendar time and on age. So far, a rigorous mathematical calculation of the prevalence of property B has been difficult, which has limited the use of the model in epidemiology and public health. We develop a partial differential equation (PDE) that simplifies the use of the three-state model. To demonstrate the validity of the PDE, it is applied to two simulation studies, one about a hypothetical chronic disease and one about dementia in Germany. In two further applications, the PDE may provide insights into smoking behaviour of males in Germany and the knowledge about the ovulatory cycle in Egyptian women.
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Citations
Jan 28, 2018·Lifetime Data Analysis·Ralph Brinks, Annika Hoyer
Dec 18, 2019·PloS One·Annika HoyerRalph Brinks
Feb 7, 2017·PloS One·Pavithra VijayakumarMeda E Pavkov
Jun 30, 2019·BMC Public Health·Ralph BrinksAnnika Hoyer
Jun 14, 2019·The International Journal of Biostatistics·Severin Guy MahianeEline Korenromp
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Jan 19, 2021·BMJ Open Diabetes Research & Care·Thaddäus TönniesAnnika Hoyer
Oct 13, 2021·Population Health Metrics·Thaddäus TönniesAnnika Hoyer