Infertility Stability Analysis, Control And Hiv Model

In this paper, we establish and analyze infertility models with competitive reproduction interference and an HIV model with vertical transmission. More precisely,First, we propose an infertility model with competitive reproduction interference and sexual structure. For the case with male and female infertility, we study the existence of a unique equilibrium and its local stability and analyze its global stability with numerical simulation. For the case with female infertility, we study the existence and global stability of the equilibria. It turns out that the strategy with both male and female infertility is more effective on depressing the rodent population.Second, we build an infertility model with competitive reproduction interference and both density-dependent birth and death rates. We study the existence of equilibrium, ana-lyze their local stability by applying the Routh-Hurwitz criterion and the globally asymptotic stability with the help of the Bendixson-Dulac criterion. We also use numerical simulation to demonstrate the validity of the results and illustrate the effects of the parameters on the dynamics.Finally, we propose an HIV model with vertical transmission and disease-related death. We find the basic reproduction number and use it to establish the existence of disease-free equilibrium and the endemic equilibrium. Then, we apply theories including that of second additive compound matrices to obtain sufficient conditions on the global stability of the equilibria.