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Bifurcation Analysis and Vaccination Strategies in Toxoplasma Gondii Dynamics Modeling for the Cat Population |
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PP: 359-384 |
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doi:10.18576/pfda/120208
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Author(s) |
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Muhammad Farman,
Aqeel Ahmad,
Muhammad Sohaid,
Evren Hincal,
Aseel Smerat,
Heba Elhaddad,
Mohamed Hafez,
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Abstract |
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| This research introduces a new fractional-order mathematical framework to explore the spread dynamics of Toxoplasma gondii between the cat population and the environment, considering the combined effects of vaccination and sanitation. To reflect the memory-dependent and hereditary nature of biological interactions, the traditional integer-order system is reformulated through the Atangana-Baleanu-Caputo (ABC) fractional derivative. A qualitative analysis of the system establishes the conditions for the validations of newly developed model including the quantitative analysis on disease-free equilibrium for study state. Furthermore, bifurcation analysis demonstrates that the system can exhibit both forward and backward bifurcations, governed by factors such as vaccination intensity, sanitation efficacy, and fractional order values. These bifurcations indicate the possible coexistence of multiple equilibrium states and the emergence of complex transitional dynamics in disease transmission. Utilizing the ABC operator for possible solutions of the fractional order model that allows the model to capture infection persistence for control strategies more realistically. Simulation outcomes reveal that decreasing fractional orders enhances memory effects, resulting in slower but more persistent infection patterns. Overall, applying the ABC fractional modeling approach provides deeper insight into the nonlinear, memory-driven, and bifurcating behavior of T. gondii transmission and supports the development of robust, long-term control measures within cat populations. |
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