A STAGE-STRUCTURED SI ECO-EPIDEMIOLOGICAL MODEL WITH TIME DELAY AND IMPULSIVE CONTROLLING

This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ＇pest-eradication＇ periodic solution and permanence of the system depend on time delay, hence, the authors call it ＂profitless＂. Further, the authors present a pest management strategy in which the pest population is kept under the economic threshold level （ETL） when the pest population is uniformly persistent. By numerical analysis, the authors also show that constant maturation time delay for the susceptible pests and pulse releasing of the infectious pests can bring obvious effects on the dynamics of system.

Natural selection bet ween two games with environmentai feedback

Evolutionary game theory has extensively investigated situations in which several gamesare competing against each other at the same time,but the model only assumes sym-metric interactions in homogeneous environments.Now,the population is consideredin heterogeneous environments,individuals in the population occupy a different qualityof patches,and individual fitness depends not only on the interaction between individ-uals,but also on the quality of the environment.Here,by establishing a mathemati-cal framework,we analyze the natural selection between two strategies and two gamesin heterogeneous environments.Furthermore,we analyze the natural selection of Pris-oner's Dilemma and Hawk-Dove games theoretically to demonstrate the dynamics ofcooperators and defectors in their choice of environment and their respective games.Asexpected,the distribution of games and strategies changes with time.Based on differentinitial population compositions,we also discuss the invasion problem of games from dif-ferent perspectives.To one's surprise,we can find that good quality patches attract allindividuals;the long-term dynamics in invariant rich environments is the same as thedynamics of symmetric interactions in homogeneous environments.

A novel SNP-set analytical method without distinguishing common variants or rare variants in genome-wide association study

Single nucleotide polymorphism (SNP)-set analysis in genome-wide association studies (GWASs)has become a hot topic.Most existing SNP-set analystic methods are designed and work well according to the different natures of common or rare variants and associated diseases.But the information that the disease associated variants are common or rare cannot be gained in advance.Therefore,in this research,we proposed a new and powerful weighted function method without distinguishing common or rare variants to select tagging SNP-set.We applied our selection method to sequence kernel associa- tion test (SKAT)and compared the power with some existing methods.The simulation results showed that our method has higher power not only than SKAT in un-weighted case,but also than SKAT in other weighted functions.Moreover,the power is improved significantly when the minor allele frequency (MAF)of causal SNP is relatively small.

THE DYNAMICS AND THERAPEUTIC STRATEGIES OF A SEIS EPIDEMIC MODEL

Based on an epidemic model which Manvendra and Vinay [Mathematical model to simulate infections disease, VSRD-TNTJ 3（2） （2012） 60 68] have proposed, we consider the dynamics and therapeutic strategy of a SEIS epidemic model with latent patients and active patients. First, the basic reproduction number is established by applying the method of the next generation matrix. By means of appropriate Lyapunov functions, it is proven that while the basic reproduction number 0 〈 R0 〈 1, the disease-free equilibrium is globally asymptotically stable and the disease eliminates; and if the basic reproduction number R0 〉 1, the endemic equilibrium is globally asymptotically stable and therefore the disease becomes endemic. Numerical investigations of their basin of attraction indicate that the locally stable equilibria are global attractors. Second, we consider the impact of treatment on epidemic disease and analytically determine the most effective therapeutic strategy. We conclude that the most effective therapeutic strategy consists of treating both the exposed and the infectious, while treating only the exposed is the least effective therapeutic strategy. Finally, numerical simulations are given to illustrate the effectiveness of the proposed results.

THE DYNAMICAL MODELS OF ACTIVATED SLUDGE SYSTEM： STOCHASTIC CELLULAR AUTOMATON AND DIFFERENTIAL EQUATIONS

A stochastic celhflar automaton （CA） model for activated sludge system （ASS） is for- mulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary differential equations （ODEs） of ASS. CA system performed by empirical parameters can reflect the characteristics of fluctuation, com- plexity and strong non-linearity of ASS. The results show that the predictions of CA are approximately similar to the dynamical behaviors of ODEs. Based on the extreme experimental system with complete cell recycle in model validation, the dynamics of biomass and substrate are predicted accurately by CA, but the large errors exist in ODEs except for integrating more spatially complicated factors. This is due to that the strong mechanical stress from spatial crowding effect is ignored in ODEs, while CA system as a spatially explicit model takes account of local interactions. Despite its extremely simple structure, CA still can capture the essence of ASS better than ODEs, thus it would be very useful in predicting long-term dynamics in other similar systems.