Stability dynamics of a delayed generalized Chikungunya virus infection model

Global stability of a delayed adaptive immunity viral infection with two routes of infection and multi-stages of infected cells

In a neuronal system, propagation speed of neuronal information is mainly determined by the length, the diameter, and the kind of the axons between the neurons. Thus, some communications between neurons are not instantaneous, and others are instantaneous or with some negligible delay. In the past years, effects of time delay on neuronal dynamics, such as synchronization, stochastic resonance, firing regularity, etc., have been investigated. For stochastic resonance, it has been reported recently that stochastic multi-resonance in a neuronal system can be induced by time delay. However, in these studies, time delay has been introduced to every connection of the neuronal system. As mentioned in the beginning, in a real neuronal system, communication between some neurons can be instantaneous or with some negligible delays. Thus, considering the effect of partial time delay (time delay is called as partial time delay if only part of connections are delayed) on neuronal dynamics could be more meaningful.In this paper, we focus on discussing effect of partial time delay on response amplitude of a Watts-Strogatz neuronal network which is locally modeled by Rulkov map. With the numerically obtained results, we can see that partial time delay can induce a stochastic multi-resonance which is indicated by the multi-peak characteristics in the variation of response amplitude with partial time delay. Namely, partial time delay could also induce stochastic multi-resonance in a neuronal system. Moreover, we also find that optimal response amplitude can be reached in much wider range of the partial time delay value when delayed connections are less (i.e., the partial time delay probability is small). This is different from the case in which all connections are delayed, where response amplitude become optimal only when time delay is nearly the multiples of external signal's period. But the range of the partial time delay value becomes narrower and narrower with the increasing of the partial time delay probability and when the partial time delay probability is large enough, response amplitude becomes optimal only when time delay is nearly the multiples of external signal period. It is similar to the case where all connections are delayed. Furthermore, effects of random rewiring probability and total link number in the neuronal network on partial time delay induced stochastic multi-resonance are also studied. It is found that partial time delay induced stochastic multi-resonance is robust to random rewiring probability but not robust to total link number. Stochastic resonance is a very important nonlinear phenomenon in neuroscience, thus, our obtained results could have some implications in this field.

We investigate general HIV infection models with three types of infected cells: latently infected cells, long-lived productively infected cells, and short-lived productively infected cells. We incorporate three discrete or distributed time delays into the models. Moreover, we consider the effect of humoral immunity on the dynamical behavior of the HIV. The HIV-target incidence rate, production/proliferation, and removal rates of the cells and HIV are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive two threshold parameters which fully determine the existence and stability of the three steady states of the model. Using Lyapunov functionals, we establish the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.

This paper studies the global stability of two discrete-time HIV infection models. The models integrate (i) latently infected cells, (ii) long-lived chronically infected cells and (iii) short-lived infected cells. The second model generalizes the first one by assuming that the incidence rate of infection as well as the production and removal rates of the HIV particles and cells are modeled by general nonlinear functions. We discretize the continuous-time models by using a nonstandard finite difference scheme. The positivity and boundedness of solutions are established. The basic reproduction number is derived. By using the Lyapunov method, we prove the global stability of the models. Numerical simulations are presented to illustrate our theoretical results.

Closed-loop identification with routine operating data: Effect of time delay and sampling time

This study establishes a novel time-delay fractional SEIHR infectious disease model to investigate the effects of saturated incidence rates and time delays on different populations, including susceptibles, infected individuals, recovered individuals, and latent infected individuals. First, the existence and boundedness of the model’s solutions are verified, confirming its well-posedness. Subsequently, the existence of equilibria is analyzed, and the impact of parameter variations on the system is explored by examining the equilibria ϵ0 and ϵ∗, as well as the basic reproduction number R0. Additionally, the global dynamics of the equilibria are further analyzed using the Lyapunov method, while Hopf bifurcation theory is applied to explore the conditions under which the system shifts from stability to oscillatory behavior. Numerical simulations further validate the theoretical analysis, showing that time-delay effects significantly influence the system’s responsiveness and the rate of disease transmission. Moreover, when the time delay τ crosses the critical threshold τ0, the system exhibits periodic oscillations. By predicting periodic fluctuations and incorporating memory effects and persistent influences, we can better control epidemics, emphasizing the importance of time-delay adjustments and enhancing the system’s biological realism.

The effect of pre-analytical handling on the stability of fractalkine, monocyte chemoattractant protein 1 (MCP1), interleukin 6 and interleukin 8 in samples of human cerebrospinal fluid

Anaerobic digestion of municipal and animal wastes provides a potentially important means of producing energy sustainably. The reliable production of methane from anaerobic digestion requires that bacteria metabolise municipal and agricultural wastes to produce mainly carbon dioxide and methane. Our model uses Monod based kinetics and is complex since the biomass concentration growth is inhibited with the increase in substrate. The production of methane depends on the number of methanogenic bacteria; there is evidence from previous chemostats experiments that there is a time delay in population number of these cells to respond to changes in substrate concentrations. In this article we focus on determining the dynamical response of the methane production rate under different dynamics of feed conditions and temperatures. Since there is a delay in the methane bacteria mass response, we include the effects of the delay on the dynamics of the system based on modification of kinetics in a simple fermentation anaerobic model. We compare the dynamics of the system with and without delay to show the contribution of delay to the overall stability of the system. References O. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi, J. P. Steyer. Dynamical model development and parameter identification for an anaerobic wastewater treament process. Biotechnol. Bioeng. 75:424–438, 2001. doi:10.1002/bit.10036 T. F. Thingstad and T. I. Langeland. Dynamics of chemostat culture: The effect of a delay in cell response. J. Theor. Biol. , 48:149–159, 1974. doi:10.1016/0022-5193(74)90186-6 J. R. Beddington and R. M. May. Time delays are not nessarily destabilizing. Math. Biosci. 27:109–119, 1975. doi:10.1016/0025-5564(75)90028-0 K. Y. San and G. Stephanopoulos. The effect of growth rate delays in substrate-inhibited kinetics on the optimal profile of fed-batch reactors. J. Theor. Biol. 28:356–361, 1986. doi:10.1002/bit.260280308 G. Stephanopoulos and K. Y. San. Studies on-line bioreactor identification. I. Theory. Biotechnol. Bioeng. 26:1176–1188, 1984. doi:10.1002/bit.260261006 A. A. Khan, A. J. Stacey and J. J. Shepherd. Optimization of methane output for an anaerobic waste digester. ANZIAM J. 54:C523–C539, 2013. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6322 J. F. Andrews. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnol. Bioeng. 10:707–723, 1968. doi:10.1002/bit.260100602 D. J. Batstone, J. Keller, I. Angelidaki, S. V. Kalyuzzhni, S. G. Pavlostathis, A. Rozzi, W. T. M. Sanders, H. Siegrist, and V. A. Vavilin. Anaerobic digestion model No. 1 (ADM1). Water Sci. Technol. 45(10):65–73, 2002 http://wst.iwaponline.com/content/45/10/65 K. J. Beers. Numerical methods for chemical engineering: Applications in Matlab . Cambridge, New York, USA, 2007. http://www.cambridge.org/us/academic/subjects/engineering/chemical-engineering/numerical-methods-chemical-engineering-applications-matlab J. F. Andrews. The development of a dynamic model and control strategies for the anaerobic digestion process. In Mathematical Models in Water Pollution Control , A. James (ed). Wiley, 1978. A. W. Bush and A. E. Cook. The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater J. Theor. Biol. 63:385–395, 1976. doi:10.1016/0022-5193(76)90041-2 L. F. Shampine, I. Gladwell and S. Thompson. Solving ODEs with Matlab . Cambridge, New York, USA, 2003. http://www.cambridge.org/us/academic/subjects/mathematics/numerical-analysis/solving-odes-matlab?format=PB

In this paper, we establish a stochastic dynamical grazing ecosystem with time delays and fluctuations. The effects of time delay, Gaussian noise and Lévy noise on the stationary probability distribution (SPD), the mean first passage time (MFPT) and stochastic resonance (SR) are analyzed. Our research results show the following: (i) For small time delay, the increasing Gaussian noise intensity leads to catastrophic regime shift (CRS) from high vegetation state to low vegetation state, while the increasing Lévy noise intensity contributes to the recovery of these shifts. For large time delay, the increasing Gaussian noise intensity or Lévy noise intensity causes the CRS phenomenon, the larger the time delay, the more frequent the CRS phenomenon. (ii) The increasing Gaussian noise intensity can diminish the stability of the high vegetation state and low vegetation state, the increasing Lévy noise intensity and Lévy stability index can enhance the stability of the high vegetation state and diminish the stability of the low vegetation state. The increasing Lévy noise intensity can lead to noise-enhanced stability (NES) of the high vegetation state, and the larger the time delay, the more pronounced the NES phenomenon. (iii) The increase of time delay can weaken SR phenomenon when signal-to-noise ratio (SNR) is a function of Gaussian noise intensity and Lévy noise intensity.

In this paper, we consider a viral infection dynamics model with immune impairment and time delay in immune expansion. By calculation, it is shown that the model has three equilibria: infection-free equilibrium, immunity-inactivated infection equilibrium, and immunity-activated infection equilibrium. By analyzing the distributions of roots of corresponding characteristic equations, the local stability of the infection-free equilibrium and the immunity-inactivated infection equilibrium is established. Furthermore, we discuss the existence of Hopf bifurcation at the immunity-activated infection equilibrium. Sufficient conditions are obtained for the global asymptotic stability of each feasible equilibria of the model by using LaSalle’s invariance principle and iteration technique, respectively. Numerical simulations are carried out to illustrate the main theoretical results.

Chikungunya virus (CHIKV) is a mosquito-borne alphavirus that causes chikungunya fever, a severe, debilitating disease that often produces chronic arthralgia. Since 2004, CHIKV has emerged in Africa, Indian Ocean islands, Asia, Europe, and the Americas, causing millions of human infections. Central to understanding CHIKV emergence is knowledge of the natural ecology of transmission and vector infection dynamics. This review presents current understanding of CHIKV infection dynamics in mosquito vectors and its relationship to human disease emergence. The following topics are reviewed: CHIKV infection and vector life history traits including transmission cycles, genetic origins, distribution, emergence and spread, dispersal, vector competence, vector immunity and microbial interactions, and co-infection by CHIKV and other arboviruses. The genetics of vector susceptibility and host range changes, population heterogeneity and selection for the fittest viral genomes, dual host cycling and its impact on CHIKV adaptation, viral bottlenecks and intrahost diversity, and adaptive constraints on CHIKV evolution are also discussed. The potential for CHIKV re-emergence and expansion into new areas and prospects for prevention via vector control are also briefly reviewed.

Telementoring allows a less experienced surgeon to benefit from an expert surgical consultation, reducing cost, travel, and the learning curve associated with new procedures. However, there are several technical limitations that affect practical applications. One potentially serious problem is the time delay that occurs any time data are transferred across long distances. To date, the effect of time delay on surgical performance has not been studied. A two-phase trial was designed to examine the effect of time delay on surgical performance. In the first phase, a series of tasks was performed, and the numbers of robotic movements required for completion was counted. Programmed incremental time delays were made in audiovisual acquisition and robotic controls. The number of errors made while performing each task at various time delay intervals was noted. In the second phase, a remote surgeon in Baltimore performed the tasks 9000 miles away in Singapore. The number of errors made was recorded. As the time delay increased, the number of operator errors increased. The accuracy needed to perform remote robotic procedures was diminished as the time delay increased. A learning curve did exist for each task, but as the time delay interval increased, it took longer to complete the task. Time delay does affect surgical performance. There is an acceptable delay of <700 msec in which surgeons can compensate for this phenomenon. Clinical studies will be needed to evaluate the true impact of time delay.

Aqueous xanthan gum solutions are non-Newtonian fluids, pseudoplastic fluids possessing yield stress. Their continuous mixing is an extremely complicated phenomenon exhibiting non idealities such as channeling, recirculation and stagnation. To characterize the continuous mixing of xanthan gum solutions, three dynamic models were utilized: (1) a dynamic model with 2 time delays in discrete time domain, (2) a dynamic model with 2 time delays in continuous time domain, and (3) a simplified dynamic model with 1 time delay in discrete time domain. A hybrid genetic algorithm was employed to estimate the model parameters through the experimental input-output dynamic data. The extents of channeling and fully-mixed volume were used to compare the performances of these three models. The dynamic model parameters exerting strong influence on the model response were identified. It was observed that the models with 2 time delays gave a better match with the experimental results.

In this paper we propose and analyze an HCV dynamics model taking into consideration the cure of infected hepatocytes and antibody immune response. We incorporate both virus-to-cell and cell-to-cell transmissions into the model. We incorporate a distributed-time delay to describe the time between the HCV or infected cell contacts an uninfected hepatocyte and the emission of new active HCV. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive two threshold parameters which fully determine the existence and stability of the three steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states. The theoretical results are confirmed by numerical simulations.

A FitzHugh–Nagumo neuron model with cubic nonlinearity and discrete delay is considered, in which the time delay is regarded as a parameter. The effect of time delay on the linear stability and Hopf bifurcation of the model is studied. The existence, stability and direction of the local and global Hopf bifurcation are derived. Some numerical simulations are employed to validate the main results of this work.