Typhoid fever is a systemic infection caused by Salmonella Typhi and occurs predominantly in association with poor sanitation and lack of clean drinking water. Despite recent progress in water and sanitation coverage, the disease remains a substantial public health problem in many developing countries. A mathematical model for the spread of typhoid has been formulated using non linear ordinary differential equations. The model includes a special treatment function to assess the effects of limited treatment resources on the spread of typhoid. It is shown that the model has multiple equilibria and using the center manifold theory, the model exhibits the phenomenon of backward bifurcation whose implications are discussed. The results suggest the need for comprehensive and accessible treatment facilities to curtail typhoid infection.

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In this manuscript, we state and prove a theorem of a similar flavour to the Generalized Mean Value Theorem for functions of one variable. For lack of a better term, we call the theorem ``Extended Generalized Mean Value Theorem'' and we abbreviate it EGMVT.In addition, we apply Rolle's Theorem to prove the theorem. Also, we deduce some corollaries for Mean Value Theorems. In addition, the EGMVT is verified by use of an example.

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