Filtern
Schlagworte
- modelling (2) (entfernen)
Institut
- Fachbereich 7 (1)
- Mathematisches Institut (1)
Chemical plant protection is an essential element in integrated pest management and hence, in current crop production. The use of Plant Protection Products (PPPs) potentially involves ecological risk. This risk has to be characterised, assessed and managed.
For the coming years, an increasing need for agricultural products is expected. At the same time, preserving our natural resources and biodiversity per se is of equally fundamental importance. The relationship of our economic success and cultural progress to protecting the environment has been made plain in the Ecosystem Service concept. These distinct 'services' provide the foundation for defining ecological protection goals (Specific Protection Goals, SPGs) which can serve in the development of methods for ecological risk characterisation, assessment and management.
Ecological risk management (RM) of PPPs is a comprehensive process that includes different aspects and levels. RM is an implicit part of tiered risk assessment (RA) schemes and scenarios, yet RM also explicitly occurs as risk mitigation measures. At higher decision levels, RM takes further risks, besides ecological risk, into account (e.g., economic). Therefore, ecological risk characterisation can include RM (mitigation measures) and can be part of higher level RM decision-making in a broader Ecosystem Service context.
The aim of this thesis is to contribute to improved quantification of ecological risk as a basis for RA and RM. The initial general objective had been entitled as "… to estimate the spatial and temporal extent of exposure and effects…" and was found to be closely related to forthcoming SPGs with their defined 'Risk Dimension'.
An initial exploration of the regulatory framework of ecological RA and RM of PPPs and their use, carried out in the present thesis, emphasised the value of risk characterisation at landscape-scale. The landscape-scale provides the necessary and sufficient context, including abiotic and biotic processes, their interaction at different scales, as well as human activities. In particular, spatially (and temporally) explicit landscape-scale risk characterisation and RA can provide a direct basis for PPP-specific or generic RM. From the general need for tiered landscape-scale context in risk characterisation, specific requirements relevant to a landscape-scale model were developed in the present thesis, guided by the key objective of improved ecological risk quantification. In principle, for an adverse effect (Impact) to happen requires a sensitive species and life stage to co-occur with a significant exposure extent in space and time. Therefore, the quantification of the Probability of an Impact occurring is the basic requirement of the model. In a landscape-scale context, this means assessing the spatiotemporal distribution of species sensitivity and their potential exposure to the chemical.
The core functionality of the model should reflect the main problem structures in ecological risk characterisation, RA and RM, with particular relationship to SPGs, while being adaptable to specific RA problems. This resulted in the development of a modelling framework (Xplicit-Framework), realised in the present thesis. The Xplicit-Framework provides the core functionality for spatiotemporally explicit and probabilistic risk characterisation, together with interfaces to external models and services which are linked to the framework using specific adaptors (Associated-Models, e.g., exposure, eFate and effect models, or geodata services). From the Xplicit-Framework, and using Associated-Models, specific models are derived, adapted to RA problems (Xplicit-Models).
Xplicit-Models are capable of propagating variability (and uncertainty) of real-world agricultural and environmental conditions to exposure and effects using Monte Carlo methods and, hence, to introduce landscape-scale context to risk characterisation. Scale-dependencies play a key role in landscape-scale processes and were taken into account, e.g., in defining and sampling Probability Density Functions (PDFs). Likewise, evaluation of model outcome for risk characterisation is done at ecologically meaningful scales.
Xplicit-Models can be designed to explicitly address risk dimensions of SPGs. Their definition depends on the RA problem and tier. Thus, the Xplicit approach allows for stepwise introduction of landscape-scale context (factors and processes), e.g., starting at the definitions of current standard RA (lower-tier) levels by centring on a specific PPP use, while introducing real-world landscape factors driving risk. With its generic and modular design, the Xplicit-Framework can also be employed by taking an ecological entity-centric perspective. As the predictive power of landscape-scale risk characterisation increases, it is possible that Xplicit-Models become part of an explicit Ecosystem Services-oriented RM (e.g., cost/benefit level).
Scientific and public interest in epidemiology and mathematical modelling of disease spread has increased significantly due to the current COVID-19 pandemic. Political action is influenced by forecasts and evaluations of such models and the whole society is affected by the corresponding countermeasures for containment. But how are these models structured?
Which methods can be used to apply them to the respective regions, based on real data sets? These questions are certainly not new. Mathematical modelling in epidemiology using differential equations has been researched for quite some time now and can be carried out mainly by means of numerical computer simulations. These models are constantly being refinded and adapted to corresponding diseases. However, it should be noted that the more complex a model is, the more unknown parameters are included. A meaningful data adaptation thus becomes very diffcult. The goal of this thesis is to design applicable models using the examples of COVID-19 and dengue, to adapt them adequately to real data sets and thus to perform numerical simulations. For this purpose, first the mathematical foundations are presented and a theoretical outline of ordinary differential equations and optimization is provided. The parameter estimations shall be performed by means of adjoint functions. This procedure represents a combination of static and dynamical optimization. The objective function corresponds to a least squares method with L2 norm which depends on the searched parameters. This objective function is coupled to constraints in the form of ordinary differential equations and numerically minimized, using Pontryagin's maximum (minimum) principle and optimal control theory. In the case of dengue, due to the transmission path via mosquitoes, a model reduction of an SIRUV model to an SIR model with time-dependent transmission rate is performed by means of time-scale separation. The SIRUV model includes uninfected (U) and infected (V ) mosquito compartments in addition to the susceptible (S), infected (I) and recovered (R) human compartments, known from the SIR model. The unknwon parameters of the reduced SIR model are estimated using data sets from Colombo (Sri Lanka) and Jakarta (Indonesia). Based on this parameter estimation the predictive power of the model is checked and evaluated. In the case of Jakarta, the model is additionally provided with a mobility component between the individual city districts, based on commuter data. The transmission rates of the SIR models are also dependent on meteorological data as correlations between these and dengue outbreaks have been demonstrated in previous data analyses. For the modelling of COVID-19 we use several SEIRD models which in comparison to the SIR model also take into account the latency period and the number of deaths via exposed (E) and deaths (D) compartments. Based on these models a parameter estimation with adjoint functions is performed for the location Germany. This is possible because since the beginning of the pandemic, the cumulative number of infected persons and deaths
are published daily by Johns Hopkins University and the Robert-Koch-Institute. Here, a SEIRD model with a time delay regarding the deaths proves to be particularly suitable. In the next step, this model is used to compare the parameter estimation via adjoint functions with a Metropolis algorithm. Analytical effort, accuracy and calculation speed are taken into account. In all data fittings, one parameter each is determined to assess the estimated number of unreported cases.