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Mathematical Modeling of CTL Delay and Human Fertility Decline



Mathematical Modeling of CTL Delay and Human Fertility Decline


Shaun Stipp

Doctor of Philosophy in Ecology and Evolutionary Biology

University of California, Irvine, 2015

Professor Dominik Wodarz, Chair

Mathematical and computational models are invaluable tools that enable one to explore the implications of the assumptions one makes about how complex systems operate. In Chapter 1, mathematical models are used to address the question of whether a delay in CTL (cytotoxic T lymphocyte) arrival to the site of an infection can increase the chances of the CTL clearing this infection. The results of three models of increasing complexity imply that there are conditions in which such an advantage of a CTL delay can occur. The mechanism for this advantage as suggested by the models is that as the infection progresses, the virus depletes its source of growth, allowing the CTL to drive the infection to lower levels. In addition, when the rate of CTL activation is proportional to the level of viral antigen, a delay is advantageous in that a higher virus load results in the activation of more CTL. Chapter 2 uses mathematical and computational models to address the phenomenon of human fertility decline. We assume a framework in which two populations—high- and low-fertility—can convert members of the other population into members of its own. We find that when the low-fertility individuals are favored in the conversion process, the low-fertility population can dominate the high-fertility population when the rate of cultural transmission is high and mortality is low. Chapter 3 investigates the matter of fertility decline in a framework where a continuum of fertilities is possible. Individuals take the weighted average of the fertility of individuals around them with copying error. Outcomes of long-term fertility are investigated with different model assumptions relating to how individuals are assigned a weight in the average. Although the qualitative behavior of the time series of fertility and the influence of parameters on it vary depending on model assumptions, the most general and relevant insight of the models is that long-term fertility is lower under conditions of low mortality.

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