Stability property of the boundary equilibria of a symbiotic model of commensalism and parasitism with harvesting in commensal populations

This article demonstrates the stability property of two boundary equilibria of a symbiotic model of commensalism and parasitism with harvesting in the commensal population. The model was proposed by Nurmaini Puspitasari, Wuryansari Muharini Kusumawinahyu, Trisilowati (2021). We first give two numeric examples to show that the corresponding results of the mentioned paper may be incorrect. Then, by analysis of the characteristic roots of the characteristic equations, we obtain sufficient conditions that ensure the locally asymptotic stability of the equilibria. After that, by applying the standard comparison theorem, some novel results on the global attractivity of these two equilibria are obtained respectively. Our results complement and supplement some known results.