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In this paper, we study the complex dynamics of a spatial nonlinear predator-prey system under harvesting. A modified Leslie-Gower model with Holling type IV functional response and nonlinear harvesting of prey is considered. We perform a detailed stability and Hopf bifurcation analysis of the spatial model system and determine the direction of Hopf bifurcation and stability of the bifurcating periodic solutions. Numerical simulations were performed to figure out how Turing patterns evolve under nonlinear harvesting. Simulation study leads to a few interesting sequences of pattern formation, which may be relevant in real world situations.

Recently, the 2014 Ebola virus (EBOV) outbreak in West Africa was the largest outbreak to date. In this paper, an attempt has been made for modeling the virus dynamics using an SEIR model to better understand and characterize the transmission trajectories of the Ebola outbreak. We compare the simulated results with the most recent reported data of Ebola infected cases in the three most affected countries Guinea, Liberia and Sierra Leone. The epidemic model exhibits two equilibria, namely, the disease-free and unique endemic equilibria. Existence and local stability of these equilibria are explored. 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 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.