Mathematical modelling Treponema infection in free-ranging Olive baboons (Papio anubis) in Tanzania
Diamond Hawkins,
Roland Kusi,
Solomaya Schwab,
Idrissa S. Chuma,
Julius D. Keyyu,
Sascha Knauf,
Filipa M.D. Paciência,
Dietmar Zinner,
Jan Rychtář,
Dewey Taylor
Affiliations
Diamond Hawkins
Department of Mathematics, Bridgewater College, Bridgewater, VA 22812, USA
Roland Kusi
College of Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA
Solomaya Schwab
Department of Mathematics, Cedar Crest College, Allentown, PA 18104, USA
Idrissa S. Chuma
Tanzania National Parks (Serengeti), P.O. Box 3134 Arusha, Tanzania
Julius D. Keyyu
Tanzania Wildlife Research Institute (TAWIRI), Arusha, Tanzania
Sascha Knauf
Institute of International Animal Health/One Health, Friedrich-Loeffler-Institut, Südufer 10, 17493 Greifswald - Insel Riems, Germany; Corresponding authors.
Filipa M.D. Paciência
Cognitive Ethology Laboratory, German Primate Center, Leibniz Institute for Primate Research, 37077 Göttingen, Germany
Dietmar Zinner
Cognitive Ethology Laboratory, German Primate Center, Leibniz Institute for Primate Research, 37077 Göttingen, Germany; Department of Primate Cognition, Georg-August-Universität Göttingen, 37083 Göttingen, Germany; Leibniz Science Campus Primate Cognition, 37077 Göttingen, Germany
Jan Rychtář
Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USA; Corresponding authors.
Dewey Taylor
Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USA
Yaws is a chronic infection caused by the bacterium Treponema pallidum susp. pertenue (TPE) that was thought to be an exclusive human pathogen but was recently found and confirmed in nonhuman primates. In this paper, we develop the first compartmental ODE model for TPE infection with treatment of wild olive baboons. We solve for disease-free and endemic equilibria and give conditions on local and global stability of the disease-free equilibrium. We calibrate the model based on the data from Lake Manyara National Park in Tanzania. We use the model to help the park managers devise an effective strategy for treatment. We show that an increasing treatment rate yields a decrease in disease prevalence. This indicates that TPE can be eliminated through intense management in closed population. Specifically, we show that if the whole population is treated at least once every 5-6 years, a disease-free equilibrium can be reached. Furthermore, we demonstrate that to see a substantial decrease of TPE infection to near-elimination levels within 15 years, the whole population needs to be treated every 2-3 years.
