Mathematical Modeling of Toxoplasmosis in Cats with Two Time Delays under Environmental Effects

Sharmin Sultana, Gilberto González-Parra () and Abraham J. Arenas
Additional contact information
Sharmin Sultana: Department of Mathematics, New Mexico Tech, Leroy Place, Socorro, NM 87801, USA
Gilberto González-Parra: Department of Mathematics, New Mexico Tech, Leroy Place, Socorro, NM 87801, USA
Abraham J. Arenas: Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería 230002, Córdoba, Colombia

Mathematics, 2023, vol. 11, issue 16, 1-20

Abstract: In this paper, we construct a more realistic mathematical model to study toxoplasmosis dynamics. The model considers two discrete time delays. The first delay is related to the latent phase, which is the time lag between when a susceptible cat has effective contact with an oocyst and when it begins to produce oocysts. The second discrete time delay is the time that elapses from when the oocysts become present in the environment to when they are able to infect. The main aim in this paper is to find the conditions under which the toxoplasmosis can disappear from the cat population and to study whether the time delays can affect the qualitative properties of the model. Thus, we investigate the impact of the combination of two discrete time delays on the toxoplasmosis dynamics. Using dynamical systems theory, we are able to find the basic reproduction number R 0 d that determines the global long-term dynamics of the toxoplasmosis. We prove that, if R 0 d < 1 , the toxoplasmosis will be eradicated and that the toxoplasmosis-free equilibrium is globally stable. We design a Lyapunov function in order to prove the global stability of the toxoplasmosis-free equilibrium. We also prove that, if the threshold parameter R 0 d is greater than one, then there is only one toxoplasmosis-endemic equilibrium point, but the stability of this point is not theoretically proven. However, we obtained partial theoretical results and performed numerical simulations that suggest that, if R 0 d > 1 , then the toxoplasmosis-endemic equilibrium point is globally stable. In addition, other numerical simulations were performed in order to help to support the theoretical stability results.

Keywords: mathematical modeling; dynamical systems; toxoplasmosis; delay differential equations; multiple time delays; stability analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/16/3463/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/16/3463/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:16:p:3463-:d:1214146

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().