On a discrete epidemic model.
On a generalized time-varying SEIR epidemic model with mixed point and distributed time-varying delays and combined regular and impulsive vaccination controls.
On a stochastic SIR model
We consider a stochastic SIR system and we prove the existence, uniqueness and positivity of solution. Moreover the existence of an invariant measure under a suitable condition on the coefficients is studied.
On oscillatory pattern of malaria dynamics in a population with temporary immunity.
On stability and bifurcation of solutions of an SEIR epidemic model with vertical transmission.
On the complex formation approach in modeling predator prey relations, mating, and sexual disease transmission.
On the dynamics of a delayed SIR epidemic model with a modified saturated incidence rate.
On the Dynamics of a Two-Strain Influenza Model with Isolation
Influenza has been responsible for human suffering and economic burden worldwide. Isolation is one of the most effective means to control the disease spread. In this work, we incorporate isolation into a two-strain model of influenza. We find that whether strains of influenza die out or coexist, or only one of them persists, it depends on the basic reproductive number of each influenza strain, cross-immunity between strains, and isolation rate. We propose criteria that may be useful for controlling...
On the dynamics of a vaccination model with multiple transmission ways
In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number below unity....
On the existence of equilibrium points, boundedness, oscillating behavior and positivity of a SVEIRS epidemic model under constant and impulsive vaccination.
On the global dynamics of the cancer AIDS-related mathematical model
In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive...
On the uniform boundedness of the solutions of systems of reaction-diffusion equations.
Optimal control of an epidemic through educational campaigns.
Optimal Screening in Structured SIR Epidemics
We present a model for describing the spread of an infectious disease with public screening measures to control the spread. We want to address the problem of determining an optimal screening strategy for a disease characterized by appreciable duration of the infectiveness period and by variability of the transmission risk. The specific disease we have in mind is the HIV infection. However the model will apply to a disease for which class-age structure...
Optimization in HIV screening problems.