Optimal control strategies for an $n$-patch waterborne disease model

Obiora Cornelius Collins


Waterborne diseases are an important concern in public health, especially in communities with limited access to clean water. Different community subpopulations can require different copping strategies for the same diseases. Modeling is one method to assist understanding and the development of effective strategies. To this end, we investigated the use of meta-population models with three types of control interventions: vaccination, treatment, and water purification. Important mathematical features of the model are determined and examined. Optimal control, applied to the model, is also formulated to determine the effective strategies to reduce the spread of the disease. For example, using optimal control, a four-fold reduction in infected individuals is possible. The value of such an improvement to the communities involved would be significant.

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O.C. Collins, K.~J. Duffy. Optimal control intervention strategies using an n-patch waterborne disease model. {em Nat Resour Model}, (2016). Accepted.


O.C. Collins, K.S. Govinder. Incorporating heterogeneity into the transmission dynamics of a waterborne disease model. {em J. Theor. Biol. } 356 (2014) 133--143.


J.A.P. Heesterbeek, M.G. Roberts. The type-reproduction number $mathcal{T} $ in models for infectious disease control {em Math. Biosci. } 206 (2007) 3--10.


S. Lenhart and J.T. Workman, {em Optimal control applied to biological models}, Chapman & Hall, London, 2007.


R.L. Miller Neilan, E. Schaefer, H. Gaff, K. Renee Fisher, S. Lenhart. Modelling optimal intervention strategies for cholera {em Bull. Math. Biol.} 72 (2010) 2004--2018.


L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko, {em The mathematical theory of optimal control process}, vol 4. Gordon and Breach Science Publishers, New York, 1986.


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