Study of an epidemic model with Z-type control

In the present paper,an epidemic model with Z-type control mechanism has been pro- posed and analyzed to explore the disease control strategy on an infectious disease outbreak.The uncontrolled model can have a disease-free equilibrium and an endemic equilibrium.The expression of the basic reproduction number and the conditions for the stability of the equilibria are derived.It is also observed that the disease-free equilibrium is globally asymptotically stable if R0<1,whereas the endemic equilibrium is globally asymptotically stable if R0>1.The model is further improved by considering Z-control mechanism and investigated.Disease can be controlled by using Z-control while the basic reproduction of the uncontrolled system is greater than unity.The positivity conditions of the solutions are derived and the basin of attraction for successful implementation of Z-control mechanism is also investigated.To verify the analytical findings,extensive numerical simulations on the model are carried out.

Study of a crop-pest-natural enemy model with Z-type control——An approach to pest management

In this study,the Z-type control method is applied to an intraguild crop-pest-natural enemy model,assuming that the natural enemy can predate on both crop and pest populations.For this purpose,the indirect Z-type controller is considered in the natural enemy population.After providing the design function for the crop-pest-natural enemy model with Z-control,we find the analytical expression of the update parameter.The findings indicate that the uncontrolled system can produce chaos through perioddoubling bifurcation due to crop over-consumption by the pest population.We draw a Poincare map to confirm the occurrence of chaos and compute the maximum Lyapunov exponent.As the observations further indicate that the pest population can be controlled by using an indirect Z-control mechanism in the natural enemy population,we postulate that,if natural enemy abundance can be governed by the update parameter,any desired pest population abundance can be achieved through the proposed Z-type controller,thus controlling the pest.To verify these assertions,extensive numerical simulations are performed to explore the potential for practical application of the proposed Z-type controller.

Effect of multiple delays on the dynamics of cannibalistic prey-predator system with disease in both populations

In the present paper, we investigate a prey-predator system with disease in both prey and predator populations and the predator population is cannibalistic in nature. The model is extended by introducing incubation delays in disease transmission terms. Local stability analysis of the system around the biologically feasible equilibria is studied, The bifurcation analysis of the system around the interior equilibrium is also studied, The sufficient conditions for the permanence of the system are derived in the presence of delays. We observe that incubation delays have the ability to destabilize the cannibalistic prey-predator system. Finally, we perform numerical experiments to substantiate our analytical findings.