Global Stability of a Two Patch Cholera Model with Fast and Slow Transmission
AbstractGlobal stability of epidemic patch models is always a challenging mathematical issue. For a waterborne disease such as Cholera, we extend aВ model originated from  in three ways: we consider a two patches environment, add disease induced mortality and migration of humansВ В between the patches. We give the conditions under which the modelexhibit four different equilibria and show that their existence is based on the local basic reproduction numbers and the type-reproduction numbers of the two patches.В Using technical Lyapunov functions that combine quadractic, Volterra-type and linear functions, we prove the global asymptotic stability of both theВ disease free equilibrium and the two boundrary equilibria in the positiveВ orthant. As for the endemic equilibrium, we use a Volterra-type LyapunovВ function to prove its global stability in the positive orthant under В biologicalВ reasonable conditions on model parameters.
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