Mathematical modeling of toxoplasmosis with multiple hosts, vertical transmission and cat vaccination
Gilberto González‐Parra, Abraham J. Arenas, Benito M. Chen‐Charpentier, Sharmin Sultana
Abstract
Abstract In this paper, we present an epidemiological model to study the dynamics of toxoplasmosis in cat and mouse populations under a continuous cat vaccination program. We construct a mathematical model at the cat and mouse populations level that includes the effect of oocysts of the parasite T. gondii which causes the toxoplasmosis infection. We include vertical transmission in both populations. We prove that the basic reproduction number $${\mathcal {R}}_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> is a threshold parameter that determines the global dynamics and the outcome of the toxoplasmosis disease in the cat and population. Numerical simulations are presented to support the theoretical results and to show the impact of a vaccination program for cats. In addition, the simulations give insight on the effect of a public health program related to removing the oocysts from the environment. These simulations show the effectiveness of a constant vaccination intervention and a oocysts clearance program.