Abstract
Severe dengue outbreaks and their consequences point out the need for prognosis and control methods which can be derived by epidemiological mathematical models. In this article we develop a model to describe observed data on hospitalized dengue cases in Colombo (Sri Lanka) and Jakarta (Indonesia). Usually, the disease is epidemiologically modelled with the SIRUV model consisting of the susceptible (S), infected (I) and recovered humans (R) and the uninfected (U) and infected (V ) female mosquitos. Because we do not have any information about the mosquito population we reduce the model to a SIR model which depends on a time-dependent transmission rate β(t) and fit it to the received data sets. To solve this, optimal control theory constructed on Pontryagin’s maximum (minimum) principle is applied in order to reach the solution with numerical optimization methods. The results serve as a basis for different simulations.
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Acknowledgement
Peter Heidrich wants to thank the research fund of the University Koblenz-Landau for supporting the participation in the ECMI 2018 conference.
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Heidrich, P., Götz, T. (2019). Modelling Dengue with the SIR Model. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_22
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DOI: https://doi.org/10.1007/978-3-030-27550-1_22
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