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  4. Mathematical Modeling and Optimal Control Strategies for Toxoplasmosis with Multiple Hosts

Mathematical Modeling and Optimal Control Strategies for Toxoplasmosis with Multiple Hosts

MMC.
2026;
Volume 13, Number 1
: pp. 60–76
Received: September 29, 2025
Accepted: January 16, 2026

Ouyadri M., El Koufi A., Belhdid S.  Mathematical Modeling and Optimal Control Strategies for Toxoplasmosis with Multiple Hosts.  Mathematical Modeling and Computing. Vol. 13, No. 1, pp. 60–76 (2026)

Authors:
  1. M. Ouyadri
  2. A. El Koufi
  3. S. Belhdid
1
Laboratory of Informatics, Mathematics and its Application, Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco
2
High School of Technology, Ibn Tofail University, Kenitra, Morocco
3
Laboratory of Fundamental Mathematics and their Applications, Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco

Toxoplasmosis is one of the most prevalent infectious diseases in the world due to its harmful effects on both humans and animals.  In this study, we present the dynamics of Toxoplasmosis in cat and mouse populations.  We implement continuous vaccination for cats, horizontal transmission in both populations, and include vertical (congenital) transmission only in the cat population.  Additionally, we consider the impact of oocysts of the parasite Toxoplasma gondii, which is responsible for causing the Toxoplasmosis infection.  The paper offers a comprehensive analysis of positivity, boundedness, and stability of equilibrium points.  Furthermore, we propose a controlled system accompanied by two suggested control strategies that aim to minimize the infected population while optimizing costs.  To support the analytical findings, a numerical example is provided.

Toxoplasma gondii
vaccination
stability analysis
vertical transmissions
horizontal transmissions
optimal control
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