Hopf bifurcation and optimal control of a delayed SLBPS virus-patch model
Xiaodong Yu, Anwar Zeb, Guiyun Liu
Abstract
This paper formulates a Susceptible–Latent–Breaking out–Patched–Susceptible (SLBPS) virus propagation model with delay of temporary immunity. The influence of time delay on stability of the model is examined by analyzing the distribution of eigenvalues of the characteristic equation. Furthermore, we also demonstrate the direction and stability of the Hopf bifurcation. Lastly, optimal control strategies in terms of the rate at which susceptible, latent, break out nodes acquiring patches to improve performance of the model are presented. For the sake of the correctness of the theoretical analysis, some numerical simulations are also presented.
Topics & Concepts
Hopf bifurcationCorrectnessEigenvalues and eigenvectorsStability (learning theory)BifurcationControl theory (sociology)MathematicsApplied mathematicsOptimal controlSaddle-node bifurcationComputer scienceControl (management)PhysicsMathematical optimizationAlgorithmArtificial intelligenceQuantum mechanicsMachine learningNonlinear systemMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsFractional Differential Equations Solutions