Uncertainty quantification on a spatial Markov-chain model for the progression of skin cancer

Vermolen, F.J.; Pölönen, Ilkka

doi:10.1007/s00285-019-01367-y

Cited by 6 publications

(4 citation statements)

References 27 publications

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“…This is summarised in Theorem 1, of which a similar version was proved in [13] Theorem 1: Let node i possess neigbours N I i (t) that are infected. Then, assuming the contact intensity matrix not to change during the time interval (t, t + τ ), the effective probability rate in the exponential distribution for node i to become infected is given by…”

Section: The Transfer Of the Virus From Individual To Individualmentioning

confidence: 83%

A Spatial Markov Chain Cellular Automata Model for the Spread of Viruses

Vermolen¹

2022

Computer Methods, Imaging and Visualization in Biomechanics and Biomedical Engineering II

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In this paper a Spatial Markov Chain Cellular Automata model for the spread of viruses is proposed. The model is based on a graph with connected nodes, where the nodes represent individuals and the connections between the nodes denote the relations between humans. In this way, a graph is connected where the probability of infectious spread from person to person is determined by the intensity of interpersonal contact. Infectious transfer is determined by chance. The model is extended to incorporate various lockdown scenarios. Simulations with different lockdowns are provided. In addition, under logistic regression, the probability of death as a function of age and gender is estimated, as well as the duration of the disease given that an individual dies from it. The estimations have been done based on actual data of RIVM (from the Netherlands).

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Section: The Transfer Of the Virus From Individual To Individualmentioning

confidence: 83%

A Spatial Markov Chain Cellular Automata Model for the Spread of Viruses

Vermolen¹

2022

Computer Methods, Imaging and Visualization in Biomechanics and Biomedical Engineering II

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“…It has been demonstrated as an effective approach to explore the regional dynamics which are inherent in the data of interest [87]. The spatial Markov chain model has also been widely utilized in the area of economics, geology, environment, public health, and engineering [88], such as soil erosion [89], obesity rate [90], drought class transition [91], temporal and spatial evolution of skin cancer [92], etc. Based on Markov chain analysis and the condition of the spatial lag type of RNCUE in the initial year, N models can be formed as an N × N conditional probability transfer matrix (Table 4), and then we can analyse the probability of improving and reducing the RNCUE in a certain region under different geographical spatial backgrounds.…”

Section: Methodsmentioning

confidence: 99%

Spatiotemporal Evolution and Influencing Factors of the Rural Natural Capital Utilization Efficiency: A Case Study of Chongqing, China

Shi

2022

Land

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The efficient utilization and optimal allocation of natural capital play an important role in economic development and human well-being. The production process of natural capital is the input and output processing of its ecological resources and the environment. Improving the rural natural capital utilization efficiency (RNCUE) is an important goal of natural capital investment, and the efficient utilization of natural capital is an important factor for the efficient operation of the regional economy and society. This study uses the super slack-based measure (SBM) model based on undesirable outputs to measure the RNCUE, combines the exploratory data analysis method (ESDA) and spatial Markov transfer matrix to analyse the spatiotemporal evolution characteristics of efficiency, and analyses the influencing factors of the change of the RNCUE in Chongqing through a spatial econometric model. The results show that: (1) The RNCUE in Chongqing is still at a low level as a whole and there is a large space for efficiency improvement and efficient operation. There is a certain spatial dependence on the interaction of efficiency between adjacent districts and counties. (2) High-high agglomeration is concentrated in the western area of Chongqing One-hour Economic Circle, and low-low agglomeration is concentrated in Southeast and Northeast Chongqing. The probability of a large change in the RNCUE in consecutive years is small, and it is easy to form the phenomenon of “club convergence” in space. (3) The RNCUE in Chongqing has been affected by rainfall, temperature, NDVI, the per capita GDP, proportion of fixed asset investment, expenditure for agriculture, and proportion of primary industry and rural population. The influencing factors show that the spatial heterogeneity is significant. The RNCUE has a negative correlation with forest coverage and the expenditure for agriculture, is not significantly positive or negative with the proportion of the primary industry and is positively correlated with the rural population density. This study points out that we can improve the RNCUE in Chongqing by optimizing the spatial differentiation control mechanism, clarifying property rights, enhancing liquidity, and strengthening scientific and technological innovation.

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“…In the work by Vermolen and Pölönen (2020), it is proved that the likelihood of changing state depends on a simple binary states of the neighbors, which has been applied to modeling the progression of skin cancer. All lattice points in the domain are initialized to the epithelial cell state {S i = 1} or unoccupied state {S i = 0}.…”

Section: Mathematical Formalismmentioning

confidence: 99%

“…Here is the probability rate per unit of time, which is determined by biological mechanisms like cell division, mutation, infection and death. The reads as, and hence the transition probability P within a time interval of length is given by In the work by Vermolen and Pölönen ( 2020 ), it is proved that the likelihood of changing state depends on a simple binary states of the neighbors, which has been applied to modeling the progression of skin cancer. All lattice points in the domain are initialized to the epithelial cell state or unoccupied state .…”

Section: Mathematical Formalismmentioning

confidence: 99%

A Cellular Automata Model of Oncolytic Virotherapy in Pancreatic Cancer

2020

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Oncolytic virotherapy is known as a new treatment to employ less virulent viruses to specifically target and damage cancer cells. This work presents a cellular automata model of oncolytic virotherapy with an application to pancreatic cancer. The fundamental biomedical processes (like cell proliferation, mutation, apoptosis) are modeled by the use of probabilistic principles. The migration of injected viruses (as therapy) is modeled by diffusion through the tissue. The resulting diffusion-reaction equation with smoothed point viral sources is discretized by the finite difference method and integrated by the IMEX approach. Furthermore, Monte Carlo simulations are done to quantitatively evaluate the correlations between various input parameters and numerical results. As we expected, our model is able to simulate the pancreatic cancer growth at early stages, which is calibrated with experimental results. In addition, the model can be used to predict and evaluate the therapeutic effect of oncolytic virotherapy.

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Uncertainty quantification on a spatial Markov-chain model for the progression of skin cancer

Cited by 6 publications

References 27 publications

A Spatial Markov Chain Cellular Automata Model for the Spread of Viruses

A Spatial Markov Chain Cellular Automata Model for the Spread of Viruses

Spatiotemporal Evolution and Influencing Factors of the Rural Natural Capital Utilization Efficiency: A Case Study of Chongqing, China

A Cellular Automata Model of Oncolytic Virotherapy in Pancreatic Cancer

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