Keynote Speakers

My main research interests are the use of mathematical models (deterministic and stochastic, to help solve problems in Epidemiology and Ecology. Research emphasis is on application of Nonlinear Dynamical System theory for deterministic models. Phase space analysis but also stability of limit sets are important issues. For dependence on parameter values Sensitivity analysis, Bifurcation theory and in case of multiple time scale dynamics Geometric singular perturbation theory. For stochastic models numerical random simulation runs and statistical analysis of the results can be used to get insight in the long-term dynamical behaviour. The models are based on processes and mechanisms at multiple levels of organization (individuals, populations). In Ecology the predator-prey interaction and competition effects on ecosystem structure and functioning can be predicted. In Epidemiology disease transmission, spread and control as well as treatment strategies of diseases, for instance the multiple strain vector-borne human/mosquitoes Dengue fever, are important issues.

"Bifurcation analysis of homologous reinfections in two-strain Dengue model"

The dynamic behaviour of a combination of two compartmental models for vector-borne Dengue fever disease is studied. One model is a two-strain [1] model, where a secondary infection occurs by the other strain. The other sub-model is a one-strain SIRSIR model (where a secondary infection is a re-infection) [2-4]. Besides infection and recovery two epidemiological mechanisms, temporary immunity and disease enhancement or neutralization, are taken into account by model differentiates between primary and secondary infections. This study extends previous work by modeling the possibility of secondary homologous and heterologous infections. Also modelling of seasonality is described where the model becomes periodically forced. The long-term dynamics is studied by numerical bifurcation analysis using realistic parameter values for Dengue [1]. This analysis reveals how the bifurcations occurring in the original two sub-models can be distinguished. Besides the codimension-one Hopf, Tangent, Flip, Pitchfork a Torus bifurcation exists leading to chaos in a part of the parameter space. Furthermore two one-strain SIRSIR models coexist and exchange their stability with the endemic equilibrium catastrophically like in a so-called Filippov bifurcation [5,6].

References
[1] Aguiar, M., Ballesteros, S., Kooi, B.W. Stollenwerk, N. (2011). The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis. Journal of Theoretical Biology, 289:181-196.

[2] Steindorf, V., Srivastav, A.K., Stollenwerk, N., et al. (2022). Modeling secondary infections with temporary immunity and disease enhancement factor: Mechanisms for complex dynamics in simple epidemiological models. Chaos, Solitons & Fractals, 112709.

[3] Aguiar, M., Steindorf, V., Srivastav, A.K., et al. (2024). Bifurcation analysis of a two infection SIR-SIR epidemic model with temporary immunity and disease enhancement. Nonlinear Dynamics, 112:13621-13639.

[4] Steindorf, V., Srivastav, A.K. , Stollenwerk, N, et al. (2024). Beyond the biting - limited impact of explicit mosquito dynamics in dengue models. BMC Infectious Diseases, 24(1):1090.

[5] Filippov, A.F. (1964). Differential equations with discontinuous right-hand side. American Mathematical Society Translations, Series 2, AMS, Ann Arbor: 199-231.

[6] Kuznetsov, Y.A., Rinaldi, S., Gragnani A. (2003). One-parameter bifurcations in planar filippov systems. Bifurcation and Chaos, 13(8):2157-2188.