MATHEMATICAL MODELLING OF SYPHILIS IN A HETEROGENEOUS SETTING WITH COMPLICATIONS

R. B. OYENIYI, E. B. ARE, M. O. IBRAHEEM

Abstract


A non linear mathematical model is used to study
the dynamics of spread of syphilis in a heterogeneous settings
with two stages of infection. The existence and uniqueness
of the system of equation is established using lipchitz condition.
The disease free equilibrium(DFE) and endemic equilibrium(
EE) were determined. The Disease Free Equilibrium is
locally stable whenever Ro < 1 and unstable otherwise. The stability
of the Endemic Equilibrium is also analyzed using Bellman
and Cooke’s theorem. Numerical simulations are carried out, results
obtained are discussed and also graphically presented.

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