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

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

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.

Modeling the spatio-temporal dynamics of air pollution index based on spatial Markov chain model

An environmental problem which is of concern across the globe nowadays is air pollution. The extent of air pollution is often studied based on data on the observed level of air pollution. Although the analysis of air pollution data that is available in the literature is numerous, studies on the dynamics of air pollution with the allowance for spatial interaction effects through the use of the Markov chain model are very limited. Accordingly, this study aims to explore the potential impact of spatial dependence over time and space on the distribution of air pollution based on the spatial Markov chain (SMC) model using the longitudinal air pollution index (API) data. This SMC model is pertinent to be applied since the daily data of API from 2012 to 2014 that have been gathered from 37 different air quality stations in Peninsular Malaysia is found to exhibit the property of spatial autocorrelation. Based on the spatial transition probability matrices found from the SMC model, specific characteristics of air pollution are studied in the regional context. These characteristics are the long-run proportion and the mean first passage time for each state of air pollution. It is found that the probability for a particular station's state to remain good is 0.814 if its neighbors are in a good state of air pollution and 0.7082 if its neighbors are in a moderate state. For a particular station having neighbors in a good state of air pollution, the proportion of time for it to continue being in a good state is 0.6. This proportion reduces to 0.4, 0.01, and 0 for the cell of moderate, unhealthy, and very unhealthy states, respectively. In addition, there exists a significant spatial dependence of API, indicating that air pollution for a particular station is dependent on the states of the neighboring stations.

A Cellular Automata Model of Oncolytic Virotherapy in Pancreatic Cancer

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.