BackgroundUnperturbed 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.MethodsThe 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.ResultsModified 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.ConclusionsThe 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.
This paper presents a recurrent epidemic model (REM) to explore the dynamics of Internet epidemiology through the phases of susceptibility to recovery. From both theoretical and practical standpoint, it has two main differences compared to the bare worm propagation modeling. In the first place, it defines a unique stochastic model of a general infection spread. In the second place, it models the recovery process as a stochastic queueing system, which accurately partitions diagnose, quarantine, disinfection and recovery processes and complements it as a recurrent failure-repair management model, which is entirely unique. There still exists an open question to model propagation patterns of infections and accompanying recovery models needed for effectively managing the infected individuals. The REM model is a unique concept in determining the parameters for estimating the recovery efficiency of disrupted systems and for developing long-term recovery strategies under different epidemic situations. Existing infection and worm propagation models can also be used in cooperation with REM in order to analyse necessary quarantine and recovery processes. REM can also be applied for the accurate classification of the phases in epidemic dynamics and the states of affected systems in general, and also be used as a guideline for developing stochastic simulations covering various types of systems with recurrent state dynamics in order to facilitate reliability analysis of the systems.
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