Time-delayed model of immune response in plants

Neofytou, G.; Kyrychko, Yuliya N.; Blyuss, Konstantin B.

doi:10.1016/j.jtbi.2015.10.020

Cited by 14 publications

(8 citation statements)

References 61 publications

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“…We note that the boundaries of the stability crossing curves shown in Fig. 7 are analytically described by (32). Figure 8 illustrates that whilst the time delays do not affect the shape of the hysteresis curve, they can cause some extra parts of it to be unstable, which happens for smaller values of the time delay to E 1 only, and for higher values of the time delays to E 3 as well.…”

Section: Numerical Stability Analysis and Simulationsmentioning

confidence: 83%

Time-delayed model of RNA interference

Neofytou

Kyrychko

Blyuss

2017

Ecological Complexity

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RNA interference (RNAi) is a fundamental cellular process that inhibits gene expression through cleavage and destruction of target mRNA. It is responsible for a number of important intracellular functions, from being the first line of immune defence against pathogens to regulating development and morphogenesis. In this paper we consider a mathematical model of RNAi with particular emphasis on time delays associated with two aspects of primed amplification: binding of siRNA to aberrant RNA, and binding of siRNA to mRNA, both of which result in the expanded production of dsRNA responsible for RNA silencing. Analytical and numerical stability analyses are performed to identify regions of stability of different steady states and to determine conditions on parameters that lead to instability. Our results suggest that while the original model without time delays exhibits a bi-stability due to the presence of a hysteresis loop, under the influence of time delays, one of the two steady states with the high (default) or small (silenced) concentration of mRNA can actually lose its stability via a Hopf bifurcation. This leads to the co-existence of a stable steady state and a stable periodic orbit, which has a profound effect on the dynamics of the system.

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Section: Numerical Stability Analysis and Simulationsmentioning

confidence: 83%

Time-delayed model of RNA interference

Neofytou

Kyrychko

Blyuss

2017

Ecological Complexity

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“…One possible extension of the work presented in this paper is to explicitly include in the model time delays associated with plant maturation time, and with delayed propagation of the RNAi signal, as has been recently done in a simpler model of immune response to a single viral infection [86]. Another interesting phenomenon to consider is the possibility of cells being occupied by two viruses simultaneously, which would allow for a wider spectrum of interactions between the viruses and their host.…”

Section: Discussionmentioning

confidence: 99%

Mathematical model of plant-virus interactions mediated by RNA interference

Neofytou

Kyrychko

Blyuss

2016

Journal of Theoretical Biology

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Cross-protection, which refers to a process whereby artificially inoculating a plant with a mild strain provides protection against a more aggressive isolate of the virus, is known to be an effective tool of disease control in plants. In this paper we derive and analyse a new mathematical model of the interactions between two competing viruses with particular account for RNA interference. Our results show that co-infection of the host can either increase or decrease the potency of individual infections depending on the levels of cross-protection or cross-enhancement between different viruses. Analytical and numerical bifurcation analyses are employed to investigate the stability of all steady states of the model in order to identify parameter regions where the system exhibits synergistic or antagonistic behaviour between viral strains, as well as different types of host recovery. We show that not only viral attributes but also the propagating component of RNA-interference in plants can play an important role in determining the dynamics.

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“…For within-plant dynamics, Neofytou, et al. ( 2016a , 2016b ) have considered the dynamics of plant immune response to virus infections, and the role of time delays associated with plant maturation time and the propagation of a signal associated with RNA interference (RNAi) to different cells within a plant. From the perspective of control of vector-borne plant infections, several recent papers have looked at the effects of time-delayed interventions, such as roguing (i.e.…”

Section: Introductionmentioning

confidence: 99%

Effects of Vector Maturation Time on the Dynamics of Cassava Mosaic Disease

et al. 2021

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Many plant diseases are caused by plant viruses that are often transmitted to plants by vectors. For instance, the cassava mosaic disease, which is spread by whiteflies, has a significant negative effect on plant growth and development. Since only mature whiteflies can contribute to the spread of the cassava mosaic virus, and the maturation time is non-negligible compared to whitefly lifetime, it is important to consider the effects this maturation time can have on the dynamics. In this paper, we propose a mathematical model for dynamics of cassava mosaic disease that includes immature and mature vectors and explicitly includes a time delay representing vector maturation time. A special feature of our plant epidemic model is that vector recruitment is negatively related to the delayed ratio between vector density and plant density. We identify conditions of biological feasibility and stability of different steady states in terms of system parameters and the time delay. Numerical stability analyses and simulations are performed to explore the role of various parameters, and to illustrate the behaviour of the model in different dynamical regimes. We show that the maturation delay may stabilise epidemiological dynamics that would otherwise be cyclic.

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Time-delayed model of immune response in plants

Cited by 14 publications

References 61 publications

Time-delayed model of RNA interference

Time-delayed model of RNA interference

Mathematical model of plant-virus interactions mediated by RNA interference

Effects of Vector Maturation Time on the Dynamics of Cassava Mosaic Disease

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