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Spatiotemporal transmission dynamics of recent Ebola spread and outbreak in West Africa: impact of control measures

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Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation

Recently, the 2014 Ebola virus (EBOV) outbreak in West Africa is the largest outbreak to date. To understand the Ebola transmission dynamics, we formulate a compartmental epidemic model with exponentially decaying transmission rates and study the impact of control measures to basic public health using an SEIR model. The epidemic model exhibits two equilibria, namely, the disease-free and unique endemic equilibria. We have calculated the basic reproduction number through next generation matrix and studied the spatial spread of the epidemic via reaction-diffusion modeling. We do not fit the model to the observed pattern of spread rather, we use parameter values estimated in past and examine the extent to which the designed model prediction agrees with the pattern of spread seen in Guinea, Liberia and Sierra Leone, West Africa. We employ disease threshold and sensitivity analysis to determine the extent to which the predictions could have improved by better parameterization.

Numerical simulations are performed with and without control measure for the designed model system. Using central manifold theory, it is established that the transcritical bifurcation occurs when basic reproduction number passes through unity. The proposed Ebola epidemic model provides an estimate to the potential number of future cases. The model indicates that the disease will decline after peaking up if multisectorial and multinational efforts to control the spread of infection are maintained. Possible implication of the results for disease eradication and its control are discussed which suggests that proper control strategies like: (i) transmission precautions, (ii) isolation and care of infectious Ebola patients, (iii) safe burial, (iv) contact tracing with follow-up and quarantine, and (v) early diagnosis are needed to stop the recurrent outbreak. A significant reduction in infection and death cases are observed when proper control measures after two months is incorporated in the model system. Two dimensional simulation experiments show that infectious population and the number of deaths in Sierra Leone will increase up to one and a half year without control but it will decline after two years. So there is a hope to end this disaster.

Keywords Ebola epidemic model; Transcritical bifurcation; Spatial spread; Basic reproduction number; Control measures.

This talk is part of the Isaac Newton Institute Seminar Series series.

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