## A stochastic model for immunological feedback in carcinogenesis: analysis and approximations |

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### Contents

Introduction | 1 |

Immunological Response as a Factor in Carcinogenesis | 14 |

Some Unsuccessful Approaches to the Approximation Problem | 33 |

Copyright | |

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### Common terms and phrases

50 T PARAMETERS 50 VALUES FIGURE AMEAN apply assumption AVAR 50 VALUES birth and death carcinogen carcinogenesis chemotherapy collective model conditional probability CUMULANT METHOD density derived deterministic equation differential equations Dubin exact process Exact versus Approximate EXMEAN 100 VALUES immunological response Kampen's Method Kampen's Variance versus Laplace transform linearized transition probabilities mean and variance Mean versus Approximate method of linearized mutation Neyman and Scott nonlinear birth number of tumor obtained PARAMETERS L=.5 Poisson distributed probability generating function probability of extinction Quadratic Death Process quadratic mean Simulation Mean versus Simulation Variance versus SIMULATION VERSUS APPROXIMATION stationary distribution stochastic mean stochastic process Stochastic Variance Taylor series tumor cells tumor growth VALUES T VERSUS Variance for Linearized Variance versus Approximate Variance versus Simulation versus Approximate Mean versus Approximate Variance VERSUS AVAR 50 VERSUS PRAO 100 VERSUS PRXO versus Simulation Variance VERSUS X2 VERSUS XMEAN 50 VERSUS XVAR Weibull distribution XMEAN 50 VALUES