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In this research, we investigate the influence of predator harvesting on the predator–prey interaction in the presence of prey social behavior using a reaction–diffusion system subject to the Neumann boundary conditions. It has been proved that the investigated model can undergo Hopf, Turing–Hopf bifurcation, which indicates the possibility of having a homogenous/nonhomogeneous periodic solution under some conditions on the model parameters. The stability of these periodic solutions is studied using the normal form on the center of the manifold theory. The obtained mathematical results are checked numerically.

<abstract><p>In the case of an epidemic, the government (or population itself) can use protection for reducing the epidemic. This research investigates the global dynamics of a delayed epidemic model with partial susceptible protection. A threshold dynamics is obtained in terms of the basic reproduction number, where for $ R_0 &lt; 1 $ the infection will extinct from the population. But, for $ R_0 &gt; 1 $ it has been shown that the disease will persist, and the unique positive equilibrium is globally asymptotically stable. The principal purpose of this research is to determine a relation between the isolation rate and the basic reproduction number in such a way we can eliminate the infection from the population. Moreover, we will determine the minimal protection force to eliminate the infection for the population. A comparative analysis with the classical SIR model is provided. The results are supported by some numerical illustrations with their epidemiological relevance.</p></abstract>