Mathematical Modeling and Optimal Control Strategies for Toxoplasmosis with Multiple Hosts

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.