Publication Date



Open access

Degree Type


Degree Name

Doctor of Philosophy (PHD)


Mathematics (Arts and Sciences)

Date of Defense


First Committee Member

Chris Cosner

Second Committee Member

Shigui Ruan

Third Committee Member

Robert Stephen Cantrell

Fourth Committee Member

Donald L. DeAngelis


Avian influenza strains have been proven to be highly virulent in human populations, killing approximately 70 percent of infected individuals. Although the virus is able to spread across species from birds-to-humans, some strains, such as H5N1, have not been observed to spread from human-to-human. Pigs are capable of infection by both avian and human strains and seem to be likely candidates as intermediate hosts for co-infection of the inter-species strains. A co-infected pig potentially acts as a mixing vessel and could produce a new strain as a result of a recombination process. Humans could be immunologically naive to these new strains, hence making them super-strains. We propose an interacting host system (IHS) for such a process that considers three host species that interact by sharing strains; that is, a primary and secondary host species can both infect an intermediate host. When an intermediate host is co-infected with the strains from both the other hosts, co-infected individuals may become carriers of a super-strain back into the primary host population. The model is formulated as a classical susceptible-infectious-susceptible (SIS) model, where the primary and intermediate host species have a super-infection and co-infection with recombination structure, respectively. The intermediate host is coupled to the other host species at compartments of given infectious subclasses of the primary and secondary hosts. We use the model to give a new perspective for the trade-off hypothesis for disease virulence, by analyzing the behavior of a highly virulent super-strain. We give permanence conditions for a number of the subsystems of the IHS in terms of basic reproductive numbers of independent strains. We also simulate several relevant scenarios showing complicated dynamics and connections with epidemic forecasting.


Mathematical Epidemiology; Dynamical Systems; Persistence