Abstract:
A nonlinear dynamical system is proposed and qualitatively analyzed to study
the dynamics of cholera disease in a population. The basic model is extended to
include; reduce infection rate ( ), increase rate of seeking treatment ,
decrease development of achlorhydria condition ), increase recovery rate from
achlorhydria condition , increase recovery rat e(improve efficacy of the
drugs) . This leads to an optimal control problem which is qualitatively
analyzed usingPontryagin’s maximum principle. Numerical simulation of the
resulting optimal control problem is carried out to gain quantitative insights into
the implications of the model and pertinent results are displayed graphically. The
simulation reveals that a multifaceted approach to the fight against the disease is
more effective than single control strategies
