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Discontinuity, Nonlinearity, and Complexity 13(2) (2024) 257--268 | DOI:10.5890/DNC.2024.06.004

S. Hariharan$^1$, K.P. Sreesiva$^2$, L. Shangerganesh$^1$, N. Barani Balan$^2$

$^1$ Department of Applied Sciences, National Institute of Technology Goa, Goa - 403 401, India

$^2$ Department of Mathematics, Central University of Tamilnadu, Thiruvarur, Tamilnadu- 610 005, India

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Abstract

In this paper, a preventive model for the treatment of an infectious disease in two animal population, is discussed. First, we study the well-posedness of the proposed mathematical model. Then we determine the disease-free equilibrium point and basic reproductive number of the model. Further, we perform the stability analysis for the disease-free equilibrium point of the model. Next, an optimal control problem is developed to minimize the cost of treating an infected population. Optimality conditions are derived using Pontryagin's principle. Numerical results are provided to validate the theoretical results.

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