Open AccessSTABILITY ANALYSIS AND OPTIMAL VACCINATION OF A WATERBORNE DISEASE MODEL WITH MULTIPLE WATER SOURCES
Author(s) -
COLLINS O. C.,
GOVINDER K. S.
Publication year - 2016
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/nrm.12095
Subject(s) - waterborne diseases , basic reproduction number , stability (learning theory) , vaccination , optimal control , outbreak , contaminated water , epidemic model , computer science , intervention (counseling) , risk analysis (engineering) , mathematical optimization , operations research , environmental science , mathematics , environmental health , business , biology , virology , medicine , machine learning , population , chemistry , psychiatry , environmental chemistry
Waterborne diseases are among the major health problems facing the world today. This is especially true in developing countries where there is limited access to clean water. In such settings, even when multiple water sources exist, they tend to be contaminated. In this paper, we formulate a waterborne disease model where individuals are exposed to multiple contaminated water sources. The fundamental mathematical features of the model such as the basic reproduction number R 0 and final epidemic size are obtained and analyzed accordingly. The global stability analysis of the disease‐free equilibrium is performed. The model is later extended by considering vaccination as a possible control intervention strategy. An optimal control problem is constructed to investigate the existence of an optimal control function that reduces the spread of the disease with minimum cost. We support our analytical predictions by carrying out numerical simulations using published and estimated data from the recent cholera outbreak in Haiti.