Hyers Ulam stability and bifurcation control of leptospirosis disease dynamics and preventations: Modeling with singular and non-singular kernels.

3 Qualitative and quantitative analysis In this section, we will provide some essential requirements to prove the validation of our model (7) such as equilibrium points with stability, positiveness , boundedness, investigation of the invariant region, reproductive number and sensitivity of the parameters for reproductive number, 3.1 Equilibrium points and reproductive number A model’s long-term behavior is highly significant.

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