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Solve for local stability of the disease free equilibrium of equation (3.1)

It appears I couldn't locate information about "equation (3.1)" or the "disease-free equilibrium" directly from the file. Could you either describe the equation, or re-upload the file if you'd like a more in-depth exploration? 

Once I have the specifics, I can help analyze the local stability for the disease-free equilibrium.

Solve for local stability of the disease-free equilibrium of equation (3.1)

Explore the local stability of the disease-free equilibrium in a diphtheria transmission model. The analysis involves calculating the basic reproduction number (R0), utilizing the Jacobian matrix, and applying stability theorems to assess disease eradication conditions. Suitable for advanced epidemiology and mathematical biology studies.

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