Backward Bifurcation in Epidemic Models of Toxoplasma gondii: A Qualitative Analysis

Abstract

Toxoplasmosis is a parasitic disease instigated by T. gondii. T. gondii can infect every warm[1]blooded vertebrate and the proportion of the world population that is suffering from the parasitic disease is over one-third. In this work, a nonlinear epidemic model is developed to analyze how various factors can instigate backward bifurcation phenomenon in the transmission dynamics of toxoplasmosis. The model is subjected to the usability test by employing ample mathematical techniques and is found to be usable. An analytical threshold that governed T. gondii transmissibility is derived and used to study the model qualitatively. Results from the analysis establish the existence of backward bifurcation for toxoplasmosis dynamics.