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This paper concerned with a delayed diffusive eco-epidemiological model with fear effect. First, we discuss the existence and boundedness of the solution of the system. Then we give some conditions for the existence and stability of the nonnegative equilibria, and Turing instability. Furthermore, we choose the delay as bifurcation parameter to study Hopf bifurcation. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can induce the spatial pattern in the system. • We propose a delayed diffusive eco-epidemiological model with fear effect. • We have studied Hopf bifurcation and Turing bifurcation of the model. • We have discussed the global stability of the equilibria. • The results show that system can generate a wide variety of spatial patterns. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct and analyze a mathematical model for the response of T-cytotoxic lymphocytes to the Ebola virus using the Herz-tuckwill model with nonlinear Conformable order differential equations which derive from real biological data, then study the global stability of the equilibria using an appropriate Lyapunov function and the LaSalle invariance principle. Furthermore, we demonstrate the impact of the non-integer order of the model compared with the integral order. Finally consider a numerical simulation that justifies the biological hypotheses and the theory results. The numerical results provided that, the non-integer order has a great impact on the treatments of Ebola virus in this model. [ABSTRACT FROM AUTHOR]