Predator - prey model of security forces versus criminals in a contemporary Ghanaian Community

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A Predator prey model is developed from the population dynamics of security forces versus criminals in a contemporary community. Using ve major crime data covering the period of 2000 to 2010 from Ghana Statistical Service, two models were developed and a local stability analysis of the model after determination of the equilibrium points was investigated. With some assumptions, the parameters of the model are estimated and the simulation of the model for various scenarios using MATLAB is done. These simulations give the typical almost sinusoidal trajectories for both the populations of the security forces and criminals. This appears to con rm that the propagation of security forces and criminals follows the predator - prey model. It also shows that the security forces and criminal activities keeps rising and falling with time. It was observed that, by analysing the same point in sequential phases and nding the time in between them the approximate periods of the phase plane cycle is found to be 12 months. The results obtained suggest that criminal activities persist if not the introduction of voluntary guards.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfilment of the requirements for the award of the degree of M.Phil Applied Mathematics,