THE GEOMETRY OF POPULATION GENETICS

By DONALD HERNANDEZ

CONTENTS WHY AGE STRUCTURE? AN INTRODUCTION HUMAN DEMOGRAPHY: A CLASSIC DEMOGRAPHIC AGE STRUCTURE THE DEATH PROCESS FERTILITY MIGRATION MODELING TRENDS AND HABITAT CHANGES THE BASIC ELEMENTS OF A DESCRIPTION ECOLOGY LIFE TABLES JUVENILE-ADULT INTERACTION MODELING NONLINEAR VITAL RATES EPIDEMICS ESSENTIAL UNSTRUCTURED MODELING THE SINGLE EPIDEMIC OUTBREAK DISEASE ENDEMICITY THE AGE OF THE DISEASE: THE INTERNAL CLOCK CHRONOLOGICAL AGE: DEMOGRAPHY AND EPIDEMICS REFERENCES THE BASIC LINEAR THEORY THE LOTKA–MCKENDRICK EQUATION THE RENEWAL EQUATION EXISTENCE OF A SOLUTION REGULARITY THE ASYMPTOTIC BEHAVIOR THE AGE PRO?LE THE OPEN POPULATION IN?NITE MAXIMUM AGE THE LESLIE MATRIX EIGENVALUES, EIGENVECTORS AND THE CHARACTERISTIC EQUATION COMMENTS AND REFERENCES NUMERICAL METHODS FOR THE LINEAR MODEL THE METHODOLOGY OF CHARACTERISTICS EULER–RIEMANN METHODS CONVERGENCE OF ER METHODS HIGHER-ORDER METHODS UNBOUNDED MORTALITY RATES APPROXIMATION OF R AND ? NUMERICAL SIMULATIONS THE TIME-DEPENDENT CASE EXTENSION OF THE LOTKA–MCKENDRICK MODEL THE CASE OF CONVERGING RATES PERIODIC RATES STRONG AND WEAK ERGODICITY REAL-LIFE DATA AND NUMERICAL SIMULATIONS NONLINEAR MODELS A GENERAL NONLINEAR MODEL THE SOLUTION TO THE PROBLEM THE EQUILIBRIA OF THE MODEL MODELING LOGISTIC GROWTH JUVENILE-ADULT DYNAMICS MULTIPLE EQUILIBRIA IN JUVENILE-ADULT DYNAMICS THE ALLEE EFFECT A MODEL FOR CANNIBALISM STABILITY OF EQUILIBRIA THE BASIC PARADIGM OF STABILITY SOME RESULTS ON THE CHARACTERISTIC EQUATION BACK TO THE LOGISTIC MODEL ADULT-JUVENILE COMPETITION BACKWARD BIFURCATION NUMERICAL METHODS FOR THE NONLINEAR MODEL FINITE DIFFERENCES ON CHARACTERISTICS ANALYTIC REPRESENTATION OF THE SOLUTION METHODS FOR HYPERBOLIC EQUATIONS METHODS BASED ON INTEGRAL EQUATIONS GLOBAL BEHAVIOR A GENERAL APPROACH TO A CLASS OF MODELS A CLASS OF LOGISTIC MODELS SEPARABLE MODELS THE CASE A D C1 CLASS-AGE STRUCTURE FOR EPIDEMICS THE CLASSICAL KERMACK–MCKENDRICK MODEL REDUCTION OF THE SYSTEM EPIDEMIC OUTBREAK AND EXTINCTION THE SIS MODEL: ENDEMIC STATES AND STABILITY MODELING VARIABLE POPULATIONS THE BASIC SIR MODEL ENDEMIC STATES FOR THE SIR MODEL A MODEL FOR THE HIV/AIDS EPIDEMIC A MODEL FOR TUBERCULOSIS EPIDEMICS AND DEMOGRAPHY SIR AND SIS AGE-STRUCTURED MODELS ANALYSIS OF THE SIS MODEL ASYMPTOTIC STABILITY FOR THE SIS MODEL RESULTS FOR THE SIR MODEL STABILITY OF STEADY STATES FOR THE SIR MODEL