Mathematical Modeling of Toxoplasmosis Considering a Time Delay in the Infectivity of Oocysts

Gilberto González-Parra, Sharmin Sultana and Abraham J. Arenas
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Gilberto González-Parra: Department of Mathematics, New Mexico Tech, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA
Sharmin Sultana: Department of Mathematics, New Mexico Tech, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA
Abraham J. Arenas: Departamento de Matematicas y Estadistica, Universidad de Cordoba, Monteria 230002, Colombia

Mathematics, 2022, vol. 10, issue 3, 1-20

Abstract: In this paper, we study the effect of the introduction of a time delay on the dynamics of toxoplasmosis. This time delay is the elapsed time from when oocysts become present in the environment and when they become infectious. We construct a mathematical model that includes cats and oocysts in the environment. We include the effect of oocysts, since they are crucial for the dynamics of toxoplasmosis. The likelihood of the acquisition of Toxoplasma gondii infection depends on the environmental load of the parasite. Furthermore, the model considers the possibility of vaccination of the feline host. In the mathematical model, we consider directly the infection of cats through the oocysts shed by other cats. We prove that the basic reproduction number R 0 is a secondary parameter that determines the global dynamics of toxoplasmosis in cat populations. We study the effect of the time delay on the stability of the steady states. We find that the time delay cannot change the stability of the endemic state, which is an important result from the biological point of view. Numerical simulations are performed to support the theoretical results and obtain further insight into understanding toxoplasmosis dynamics in cat populations.

Keywords: mathematical model; toxoplasmosis; time delay; cats; oocysts; vaccination; simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (5)

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