Building epidemic models for living populations and computer networks.

Accurate modeling of viral outbreaks in living populations and computer networks is a prominent research field. Many researchers are in search for simple and realistic models to manage preventive resources and implement effective measures against hazardous circumstances. The ongoing Covid-19 pandemic has revealed the fact about deficiencies in health resource planning of some countries having relatively high case count and death toll. A unique epidemic model incorporating stochastic processes and queuing theory is presented, which was evaluated by computer simulation using pre-processed data obtained from an urban clinic providing family health services. Covid-19 data from a local corona-center was used as the initial model parameters (e.g. R0, infection rate, local population size, number of contacts with infected individuals, and recovery rate). A long-run trend analysis for 1 year was simulated. The results fit well to the current case data of the sample corona center. Effective preventive and reactive resource planning basically depends on accurately designed models, tools, and techniques needed for the prediction of feature threats, risks, and mitigation costs. In order to sufficiently analyze the transmission and recovery dynamics of epidemics it is important to choose concise mathematical models. Hence, a unique stochastic modeling approach tied to queueing theory and computer simulation has been chosen. The methods used here can also serve as a guidance for accurate modeling and classification of stages (or compartments) of epidemics in general.

Is cancer a pure growth curve or does it follow a kinetics of dynamical structural transformation?

BACKGROUND: Unperturbed tumor growth kinetics is one of the more studied cancer topics; however, it is poorly understood. Mathematical modeling is a useful tool to elucidate new mechanisms involved in tumor growth kinetics, which can be relevant to understand cancer genesis and select the most suitable treatment. METHODS: The classical Kolmogorov-Johnson-Mehl-Avrami as well as the modified Kolmogorov-Johnson-Mehl-Avrami models to describe unperturbed fibrosarcoma Sa-37 tumor growth are used and compared with the Gompertz modified and Logistic models. Viable tumor cells (1×105) are inoculated to 28 BALB/c male mice. RESULTS: Modified Gompertz, Logistic, Kolmogorov-Johnson-Mehl-Avrami classical and modified Kolmogorov-Johnson-Mehl-Avrami models fit well to the experimental data and agree with one another. A jump in the time behaviors of the instantaneous slopes of classical and modified Kolmogorov-Johnson-Mehl-Avrami models and high values of these instantaneous slopes at very early stages of tumor growth kinetics are observed. CONCLUSIONS: The modified Kolmogorov-Johnson-Mehl-Avrami equation can be used to describe unperturbed fibrosarcoma Sa-37 tumor growth. It reveals that diffusion-controlled nucleation/growth and impingement mechanisms are involved in tumor growth kinetics. On the other hand, tumor development kinetics reveals dynamical structural transformations rather than a pure growth curve. Tumor fractal property prevails during entire TGK.