Nonlinear dynamics of within-host parasite competition - Rethinavel, Natarajan [UNESP] (2013)
In this thesis we study the population biology of host-parasite systems, with a systematic view of the e?ects produced by multiple infections of di?erent parasites on a same host population. This situation is akin to multiple species competing for a shared resource. As parasites compete for a host, several outcomes at the population level can appear. If both parasites cannot jointly infect the same host, then the ?ttest parasite eliminates the other. When confection is possible, the pattern changes, and coexistence of both parasites becomes possible. Finally, if a parasite can displace the other within the host, the so-called intraguild e?ect, the outcome will strongly be dependent on the income rate of new hosts, which is determined by environmental factors. We studied this system through a mathematical model which is broad enough to encompass these situations. We proceed by steps: ?rst we framed a simple mathematical model for a single parasite/host case and as we progress to other cases, our mathematical model includes new terms and ?nally it is shaped into a complete model. Our methods are twofold. We study analytically the stability of the disease-free state, which allows us to give conditions for the ability of the parasites to invade a disease-free/non-infected population. On the other hand, we resort to numerical methods to study the long-term behavior of the system, which in all cases tends to a ?xed point. The main focus is to know which parasite prevails or if they are able to coexist, and determine the conditions that regulate this outcome . Through bifurcation diagrams we analyzed the importance of the richness of the environment, de?ned by the rate of production of new hosts. We found that the long-term states depend crucially on this rate. Our main original contribution is related to the study of the intraguild e?ect. Depending of the host income rate we can have four di?erent states, which are a disease...