We present a compartmental model for the dynamics of transmission of leishmaniasis that includes incidental hosts for humans which act only as sinks of infection, primary reservoir hosts for animals which act as sources and sinks of infection, and secondary reservoir hosts for sandflies which act as the liaison between primary reservoirs and incidental hosts. The stability analysis of equilibria of the model shows that the threshold conditions for disease persistence, are completely determined by the reproduction number, and do not explicitly include parameters relating to the dynamics transmission in the incidental hosts, which means that the disease becomes endemic if it persists endemically in the primary reservoir hosts, and therefore the control measures should be directed towards reservoir hosts. This is illustrated via numerical simulations of the model using parameters generated from data from Kabylie, Algeria.
In this talk, I will report our study of a reaction-diffusion Lyme disease model with seasonality. In the case of a bounded habitat, we obtain a threshold result on the global stability of either disease-free or endemic periodic solution. In the case of an unbounded habitat, we establish the existence of the disease spreading speed and its coincidence with the minimal wave speed for time-periodic traveling wave solutions. We also estimate parameter values based on some published data, and use them to study the Lyme disease transmission in Port Dove, Ontario. Some numerical simulations will present to illustrate our analytic results.
Cheyne-Stokes respiration (CSR) is a breathing pattern cycling between apnea (temporary breathing cessation) and hyperpnea (rapid and deep breathing). It is associated with neurological monitoring of blood carbon dioxide levels. Clinical researchers hypothesize that fluid shifts in the body when changing from an upright to a recumbent position are a factor involved in the onset of CSR. A model of CSR that incorporates body fluid shifts fit to clinical measurements is presented and analyzed. In agreement with clinical knowledge, the model predicts increased likelihood of CSR for males over females, and for patients in the supine position over upright.