Rich dynamics of a simple delay host-pathogen model of cell-to-cell infection for plant virus

Abstract

Viral dynamics within plant hosts can be important for understanding plant disease prevalence and impacts. However, few mathematical modeling efforts aim to characterize within-plant viral dynamics. In this paper, we derive a simple system of delay differential equations that describes the spread of infection throughout the plant by barley and cereal yellow dwarf viruses via the cell-to-cell mechanism. By incorporating ratio-dependent incidence function and logistic growth of the healthy cells, the model can capture a wide range of biologically relevant phenomena via the disease-free, endemic, mutual extinction steady states, and a stable periodic orbit. We show that when the basic reproduction number is less than 1 (R 0 < 1), the disease-free steady state is asymptotically stable. When R 0 > 1, the dynamics either converge to the endemic equilibrium or enter a periodic orbit. Using a ratiodependent transformation, we show that if the infection rate is very high relative to the growth rate of healthy cells, then the system collapses to the mutual extinction steady state. Numerical and bifurcation simulations are provided to demonstrate our theoretical results. Finally, we carry out parameter estimation using experimental data to characterize the effects of varying nutrients on the dynamics of the system. Our parameter estimates suggest that varying the nutrient supply of nitrogen and phosphorous can alter the dynamics of the infection in plants, specifically reducing the rate of viral production and the rate of infection in certain cases.

Global Dynamics and Implications of an HBV Model with Proliferating Infected Hepatocytes

“…This technique is modified from Hews et al [36]. The "blow-up transformation" has been used previously to study similar complex equilibrium [46][47][48]. Notice that a similar argument can be used for ( 7)-( 9) to prove that if R 0 > r+µ µ and r < a < µ + r, then E 0 is globally stable.…”

Dynamics and growth rate implications of ribosomes and mRNAs interaction in E. coli

“…The effects of nutrient conditions on cell growth have attracted significant modeling effort due to their wide implications, such as in the fields of ecology [36] , [37] , [38] , [39] , [40] and agriculture [41] , [42] , [43] , [44] , [45] . Furthermore, these effects introduce interesting dynamical properties extending the Lotka-Volterra framework [36] , [37] , [38] , [46] , [47] .…”

Rich Dynamics of a General Producer–Grazer Interaction Model under Shared Multiple Resource Limitations

“…For example, it has been demonstrated that E. coli uses different resource allocation strategies to maintain the same growth rate under various resource limitations [15][16][17]. Others have also shown that plant-virus dynamics are altered under different resource treatments [18][19][20][21]. Growth functions that depend on biochemical constraints often ignore most aspects of the molecular mechanisms for growth, for example, they only consider the available supplies of each resource in proportion to the others.…”