The analysis of epidemic network model with infectious force in latent and infected period.
The Basic Reproduction Number of an Infectious Disease in a Stable Population: The Impact of Population Growth Rate on the Eradication Threshold
Although age-related heterogeneity of infection has been addressed in various epidemic models assuming a demographically stationary population, only a few studies have explicitly dealt with age-specific patterns of transmission in growing or decreasing population. To discuss the threshold principle realistically, the present study investigates an age-duration-structured SIR epidemic model assuming a stable host population, as the first scheme to account for the non-stationality of the host population....
The combinatorics of evolutionary trees---a survey.
The common ancestor process for a Wright-Fisher diffusion.
The complete parameters analysis of the asymptotic behaviour of a logistic epidemic model with two stochastic perturbations.
The discrete Beverton-Holt model with periodic harvesting in a periodically fluctuating environment.
The dynamic behaviors of a new impulsive predator prey model with impulsive control at different fixed moments
In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors. Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills. Existences of the "infection-free" periodic solution and the "predator-free" solution are analyzed...
The dynamic complexity of a Holling type-IV predator-prey system with stage structure and double delays.
The dynamics of mutation-selection algorithms with large population sizes
The dynamics of the pulse birth in an SIR epidemic model with standard incidence.
The effect of impulsive diffusion on dynamics of a stage-structured predator-prey system.
The effect of spatial scale on predicting time series: a study on epidemiological system identification.
The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response
We consider a system of delay differential equations modelling the tumor-immune system competition with negative immune response and three positive stationary points. The dynamics of the first two positive solutions are studied in terms of the local stability. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence and stability of a limit cycle bifurcating from the second positive stationary point, when the delay (taken as a parameter) crosses some...
The Effects of HIV-1 Infection on Latent Tuberculosis
Tuberculosis is the leading cause of death due to infectious diseases in the world today, and it is increasing due to co-infection with HIV-1, the causative agent of AIDS. Here, we examine the impact that HIV-1 infection has on persons with latent tuberculosis. Based on previous work, we develop a mathematical model of an adaptive immune response in the lung which considers relevant immune effectors such as macrophages, various sub-populations of T-cells, and key cytokines to predict which mechanisms...
The EM algorithm and its implementation for the estimation of frequencies of SNP-haplotypes
A haplotype analysis is becoming increasingly important in studying complex genetic diseases. Various algorithms and specialized computer software have been developed to statistically estimate haplotype frequencies from marker phenotypes in unrelated individuals. However, currently there are very few empirical reports on the performance of the methods for the recovery of haplotype frequencies. One of the most widely used methods of haplotype reconstruction is the Maximum Likelihood method, employing...
The finite difference scheme for 3D mathematical modeling of a wood drying process.
The Kneser property for abstract retarded functional differential equations with infinite delay.
The pattern of genetic hitchhiking under recurrent mutation.
The periods of the Volterra-Lotka system.
The permanence and extinction of a discrete predator-prey system with time delay and feedback controls.