title: Modelling Optimal Control of Cholera in Communities Linked by Migration.
abstract: A mathematical model for the dynamics of cholera transmission with permissible controls between two connected communities is developed and analysed. The dynamics of the disease in the adjacent communities are assumed to be similar, with the main differences only reflected in the transmission and disease related parameters. This assumption is based on the fact that adjacent communities often have different living conditions and movement is inclined toward the community with better living conditions. Community specific reproduction numbers are given assuming movement of those susceptible, infected, and recovered, between communities. We carry out sensitivity analysis of the model parameters using the Latin Hypercube Sampling scheme to ascertain the degree of effect the parameters and controls have on progression of the infection. Using principles from optimal control theory, a temporal relationship between the distribution of controls and severity of the infection is ascertained. Our results indicate that implementation of controls such as proper hygiene, sanitation, and vaccination across both affected communities is likely to annihilate the infection within half the time it would take through self-limitation. In addition, although an infection may still break out in the presence of controls, it may be up to 8 times less devastating when compared with the case when no controls are in place.
authors.affiliation: Department of Mathematical Science, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa.
authors.forename: J B H
authors.initials: JB
authors.lastname: Njagarah
authors.affiliation: Department of Mathematical Science, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa.
authors.forename: F
authors.initials: F
authors.lastname: Nyabadza
mesh_terms: D000465:Algorithms; D050936:Basic Reproduction Number; D002771:Cholera / Q000453:epidemiology* / Q000635:transmission*; D003140:Communicable Disease Control; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000517:prevention & control; D004641:Emigration and Immigration; D063426:Human Migration; D006801:Humans; D006920:Hygiene; D008962:Models, Theoretical; D009010:Monte Carlo Method; D012499:Sanitation; D014611:Vaccination; D014734:Vibrio cholerae