The number of reports on mathematical modeling related to oncology is increasing with advances in oncology. Even though the field of oncology has developed significantly over the years, oncology-related experiments remain limited in their ability to examine cancer. To overcome this limitation, in this study, a stochastic process was incorporated into conventional cancer growth properties to obtain a generalized mathematical model of cancer growth. Further, an expression for the violation of symmetry by cancer clones that leads to cancer heterogeneity was derived by solving a stochastic differential equation. Monte Carlo simulations of the solution to the derived equation validate the theories formulated in this study. These findings are expected to provide a deeper understanding of the mechanisms of cancer growth, with Monte Carlo simulation having the potential of being a useful tool for oncologists.
Background: The novel emerging virus SARS-CoV-2 has affected all human-kind during the first half of 2020. The aim of the study was to survey the actual circumstances from January until May. Methods: The data are collected and released systematically, by law, from the National Epidemiological Surveillance of Infectious Disease (NESID). Findings: Analysis of these data revealed that the infection spread in Japan from late March to early April 2020. The SARS-CoV-2 infection rate at its peak was estimated to be 10%. Thus, the size of the population who may have been exposed to the novel virus in Japan is estimated at 0.2 million, which is relatively small. The number of related deaths is likely to converge on 1,000 people. Interpretation: Applying the law of large numbers allows estimation of the infection rate as well as of the size of the affected population by statistical analysis. How to collect the data must be defined before the data analysis is suggested to be important to reflect the actual circumstances about COVID-19.
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