Effect of Holling type II Function in Stage Structured Model with Maturation Delay

In order to analyze the propagation laws of computer viruses in the network, many epidemiological models have been borrowed to depict the spread of computer viruses because of the high similarity between the computer viruses and the biological population interactions. A mathematical model of plant, pest and natural enemy in a three species stage structured model was studied. It is assumed that natural enemy has two life stages; mature and immature. Pest can only feed on plant and only matured natural enemy can feed on pest. The plant-pest interaction follows of Holling type II function. Delay Σ for the transformation from immature stage to mature stage of natural enemy is also considered. The positivity and the boundedness of the model is studied. Further, equilibria of the system is discussed in two parts when τ=0 and τ ≠ 0. The stability of the model is analyzed by using Routh-Hurwitz stability criteria and Descartes rule of sign and condition of stability switch is also obtained. In the last section, numerical simulations have been done to support results. Similarly, same parameters can be incorporated in a four-compartment computer virus propagation model with two delays and graded infection rate is investigated and the critical values where a Hopf bifurcation occurs are obtained by analyzing the distribution of eigenvalues of the corresponding characteristic equation.