A study of mathematical models for reducing feral cat populations
Feral cats are an invasive species that pose environmental issues. To humanely reduce feral cat populations over time, we study sterilization campaigns by constructing three compartmental mathematical models and analyze their stability with and without sterilizations. We conduct a simulation study where we vary initial population proportions, initial population sizes, and parameters. We find that the percent adjusted rate at which the population grows is constant across initial populations sizes. We find that in our simulations without sterilizations, the ratio of adults to kittens converges. In our simulations with sterilizations, the ratio of adults to kittens grows continuously. In population models, the replacement rate is the number of adult fertile female offspring per adult fertile female. We find the replacement rate and define a supremum for either the birth or maturation rate for the population to shrink without a sterilization campaign. We find that the replacement rate is 0 for a population with sterilizations and no abandonment. With sterilization and abandonment, we define an infimum on the sterilization rate for the population to shrink while fixing the initial population, abandonment rate, and number of house cats. Our goal is to develop models that can be replicated and implemented where data is available on feral cat populations.