Eric Ávila-Vales

Stability and Hopf bifurcation in a delayed viral infection model with mitosis transmission

In this paper we study a model of HCV with saturation and delay, we stablish the local and global stability of system also we stablish the occurrence of a Hopf bifurcation. We will determine conditions for the permanence of model, and the length of delay to preserve stability. We present a sensitivity analysis for the basic reproductive number.

Solving delay differential systems with history functions by the Adomian decomposition method

Abstract A number of nonlinear phenomena in many branches of the applied sciences and engineering are described in terms of delay differential equations, which arise when the evolution of a system depends both on its present and past time. In this work we apply the Adomian decomposition method (ADM) to obtain solutions of several delay differential equations subject to history functions and then investigate several numerical examples via our subroutines in MAPLE that demonstrate the efficiency of our new approach. In our approach history functions are continuous across the initial value and its derivatives must be equal to the initial conditions (see Section 3 ) so that our results are more efficient and accurate than previous works.

Stability and bifurcation analysis of a SIR model with saturated incidence rate and saturated treatment

We study the dynamics of a SIR epidemic model with nonlinear incidence rate, vertical transmission vaccination for the newborns and the capacity of treatment, that takes into account the limitedness of the medical resources and the efficiency of the supply of available medical resources. Under some conditions we prove the existence of backward bifurcation, the stability and the direction of Hopf bifurcation. We also explore how the mechanism of backward bifurcation affects the control of the infectious disease. Numerical simulations are presented to illustrate the theoretical findings.

Turix, a dynamic mechanistic model for feed evaluation

The objective of this study was to use the Turix model (a new mechanistic dynamic model that can be used for feed evaluation under tropical conditions), along with in situ and in vitro sugar cane experimental data from a previous study, to evaluate sugar cane kinetics through estimation of three parameters associated with ruminal bacterial growth: kM,SmL, the substrate uptake; kLM, the bacterial growth from intermediate metabolite; and YVFAP,FS, the products related to volatile fatty acid yield. Values of these parameters for the whole sugar cane and its neutral detergent fiber (NDF) and acid detergent fiber (ADF) fractions were: a) kM, SmL, 16.20, 50.47 and 21.97 mL h-1 (mg M)-1 ; b) kLM, 96.00, 543.00 and 1,680.00 h-1 ; and, 1.02, 0.40 and 0.23 g g-1 , respectively. Results from the model adjustment showed a slow microbial substrate uptake c) Y VFAP, FS and a low biomass yield for whole sugar cane. The highest substrate uptake was obtained for NDF, while the highest biomass yield was obtained for ADF. The interrelation between the parameters kM, SmL showed to be important for biological and Y VFAP, FS description of microorganism growth and VFAP and biomass production.

Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form , and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings.

Mechanistic Model Evaluation of Tree Species and Cactae Commonly Consumed by Grazing Goats

Abstract Vargas-Villamil, L., Juárez-Reyes, A.S., Ku-Vera, J., Ávila-Vales, E., Vargas-Villamil, F., Medina-Peralta, S. and Cerrillo-Soto, M.A. 2008. Mechanistic model evaluation of tree species and cactae commonly consumed by grazing goats. J. Appl. Anim. Res., 33: 193–198. The mechanistic dynamic model, Kóokay, was used to estimate the initial high degradable phase (QS sc (0)), the medium degradation fractional rate (k ND,NDSm), the fermentation fractional rate (kSm,SmF) and the relation between the produced gas as a function of the fermented mass (f ΔG,ΔF). To obtain these parameters a bounded regression problem was solved using in situ and in vitro data. It was found that: the cactae had much higher value for Qsc(0), k ND,NDSm and k Sm,SmF than tree leaves. The fΔG,ΔF > 40 mLG(mgF)−1 for Q. grisea and Opuntia spp and fΔG,ΔF < 40 mLG(mgF)−1 for the others. At the incubation time of 8 h, the fermentation of the tree leaves, the O. leptocaulis and the Opuntia spp was 20, ∼35 and 60 mgF(100 mgDM)−1, respectively. It was concluded that kSm,SmF is an important parameter to determine the nutritive value of new feeds since it is useful to predict the F into the rumen. Also, the F for Q. grisea, Q. eduardii and A. schaffheri are similar, but lower than Opuntia spp and O. leptocaulis.