Considering the time for them to obtain immunity and the possibility for them to be infected before this, two SVIR models are established to describe continuous vaccination strategy and pulse vaccination strategy (PVS), respectively. It is shown that both systems exhibit strict threshold dynamics which depend on the basic reproduction number. If this number is below unity, the Acalabrutinib disease can be eradicated.

And if it is above unity, the disease is endemic in the sense of global asymptotical stability of a positive equilibrium for continuous vaccination strategy and disease permanence for PVS. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccinees to obtain immunity or the possibility for them to be infected before this is neglected, this condition disappears and the disease can always be eradicated by some suitable vaccination strategies. This may lead to over-evaluating the effect of vaccination. (c) 2007 Elsevier Ltd. All rights reserved.”
“Parental care is incorporated into a prey-predator model in which immature predators are taken care of by their parents. It is assumed that adult predators confront the problem to stay home to protect offspring or to go out to

forage. The global dynamics of the mathematical model is analyzed by means of analytical methods and numerical simulations. Conditions for the extinction of predator populations are established Selleckchem AZD4547 and the manners in which predators become extinct are revealed. Bifurcation analysis shows that the model admits changes from the

extinction of predators to stable coexistence at a positive equilibrium point, and then to stage-structure induced oscillations. It is shown that optimal invest of adult predators can be achieved. (c) 2007 Elsevier Ltd. All rights reserved.”
“We formulated a novel cellular automata (CA) model for HIV dynamics and drug treatment. The model is built upon realistic biological processes, including the virus AZD6738 order replication cycle and mechanisms of drug therapy. Viral load, its effect on infection rate, and the role of latently infected cells in sustaining HIV infection are among the aspects that are explored and incorporated in the model. We assume that the calculation of the number of cells in the neighborhood which influences the center cell’s state is based on the viral load. This variable-cell neighborhood enables the simulation of an infection rate that is correlated to the viral load. This approach leads to a new and flexible way of modeling HIV dynamics and allows for the simulation of different antiretroviral drug treatments based on their individual and combined effects.