Toxoplasma gondii establishes a chronic infection by forming cysts preferentially in the brain. This chronic infection is one of the most common parasitic infections in humans and can be reactivated to develop life-threatening toxoplasmic encephalitis in immunocompromised patients. Host-pathogen interactions during the chronic infection include growth of the cysts and their removal by both natural rupture and elimination by the immune system. Analyzing these interactions is important for understanding the pathogenesis of this common infection. We developed a differential equation framework of cyst growth and employed Akaike Information Criteria (AIC) to determine the growth and removal functions that best describe the distribution of cyst sizes measured from the brains of chronically infected mice. The AIC strongly support models in which T. gondii cysts grow at a constant rate such that the per capita growth rate of the parasite is inversely proportional to the number of parasites within a cyst, suggesting finely-regulated asynchronous replication of the parasites. Our analyses were also able to reject the models where cyst removal rate increases linearly or quadratically in association with increase in cyst size. The modeling and analysis framework may provide a useful tool for understanding the pathogenesis of infections with other cyst producing parasites. 