Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world’s human population carry a Toxoplasma infection. However, the transmi...
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Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world’s human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood, although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. The analyses based on the deterministic model are verified by stochastic simulation near the thresholds of the parameters.
Understanding how cells proliferate, migrate and die in various environments is essential in determining how organisms develop and repair themselves. Continuum mathematical models, such as the logistic equation and th...
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Understanding how cells proliferate, migrate and die in various environments is essential in determining how organisms develop and repair themselves. Continuum mathematical models, such as the logistic equation and the Fisher-Kolmogorov equation, can describe the global characteristics observed in commonly used cell biology assays, such as proliferation and scratch assays. However, these continuum models do not account for single-cell-level mechanics observed in high-throughput experiments. Mathematical modelling frameworks that represent individual cells, often called agent-basedmodels, can successfully describe key single-cell-level features of these assays but are computationally infeasible when dealing with large populations. In this work, we propose an agent-basedmodel with crowding effects that is computationally efficient and matches the logistic and Fisher-Kolmogorov equations in parameter regimes relevant to proliferation and scratch assays, respectively. This stochastic agent-basedmodel allows multiple agents to be contained within compartments on an underlying lattice, thereby reducing the computational storage compared to existing agent-basedmodels that allow one agent per site only. We propose a systematic method to determine a suitable compartment size. Implementing this compartment-based model with this compartment size provides a balance between computational storage, local resolution of agent behaviour and agreement with classical continuum descriptions.
In an effort to provide regional decision support for the public healthcare, we design a data-driven compartment-based model of COVID-19 in Sweden. From national hospital statistics we derive parameter priors, and we ...
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In an effort to provide regional decision support for the public healthcare, we design a data-driven compartment-based model of COVID-19 in Sweden. From national hospital statistics we derive parameter priors, and we develop linear filtering techniques to drive the simulations given data in the form of daily healthcare demands. We additionally propose a posterior marginal estimator which provides for an improved temporal resolution of the reproduction number estimate as well as supports robustness checks via a parametric bootstrap *** our computational approach we obtain a Bayesian model of predictive value which provides important insight into the progression of the disease, including estimates of the effective reproduction number, the infection fatality rate, and the regional-level immunity. We successfully validate our posterior model against several different sources, including outputs from extensive screening programs. Since our required data in comparison is easy and non-sensitive to collect, we argue that our approach is particularly promising as a tool to support monitoring and decisions within public ***: Using public data from Swedish patient registries we develop a national-scale computational model of COVID-19. The parametrized model produces valuable weekly predictions of healthcare demands at the regional level and validates well against several different sources. We also obtain critical epidemiological insights into the disease progression, including, e.g., reproduction number, immunity and disease fatality estimates. The success of the model hinges on our novel use of filtering techniques which allows us to design an accurate data-driven procedure using data exclusively from healthcare demands, i.e., our approach does not rely on public testing and is therefore very cost-effective.
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