Mathematical Biology Seminar
Feb 12, 12:00pm-1:00pm in MSB 318
Speaker: Brendan Shrader (UCF Department of Mathematics)
Title: The impacts of post-infection mortality and partial immunity on disease endemicity
Abstract: A number of infectious diseases, such as Q-fever, dengue, and COVID-19, can have symptoms that last weeks, months, or years after infection. In this talk, we discuss a published mass-action disease model that is motivated by these examples and incorporates post-infection mortality and partial immunity. Then, we construct a new model that uses a standard incidence rate to examine how disease dynamics depend on the incidence rate. Numerically, we find that in cases when the mass-action model has limit cycles, the standard-incidence model does not. To understand the standard-incidence model analytically, we prove the existence and uniqueness of the endemic equilibrium, prove the global stability of the disease-free equilibrium, and provide partial results about the global stability of the endemic equilibrium. We show that in parameter regimes for which limit cycles occur in the mass-action model, they do not occur in our standard-incidence model. Lastly, we discuss the relationship between partial immunity and the endemicity of infectious diseases using a simplified model, and we find a qualitative threshold for when the disease is endemic in the recovered population.
Read More