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Transmission Dynamic Response of Cholera Epidemic Model to Indirect and Direct Infectious Contact: Stability and Homotopy Analysis Method

Cholera is generally a disease of the poor affecting regions without an enlightened sense of hygiene and access to safe drinking water. In this paper, a mathematical model for cholera transmission dynamics is formulated. The cholera model formulated is designed into compartments which lead to the system of nonlinear ordinary differential equations. The model is built on the assumption that cholera is contacted indirectly through the ingestion of vibrio cholerae in contaminated water and direct acquisition with infected individual through effective infectious contact. The model is analyzed in a positively invariant region to show that it is bounded, realistic in an epidemiological sense and mathematically well posed. The basic reproduction number Rch is obtained and shown that if Rch < 1, then cholera epidemic model at the cholera-free equilibrium solutions is locally and globally asymptotically stable. The numerical solutions of the model is obtained using the Homotopy Analysis Method (HAM) and graphical illustrations were presented.