Mathematical models of in-host viral dynamics and immune response are a vital tool for patient-specific estimation of the initial viral load, prediction of the course of an infection, etc. The ...COVID-19 pandemics has given impetus to the development of models with an ever-increasing degree of complexity. We show that one of the most popular models—the Target Cell Limited model—fails the identifiability test, i.e., its parameters cannot be uniquely inferred from readily available data such as viral load measurements. We present a model that is both identifiable and parsimonious according to information criteria. Our model’s predictions match both reported observations of COVID-19 patients and predictions of its more complex counterparts.
Pine wilt disease is caused by nematodes transmitted by pine sawyer beetles and is fatal for several pine species. The trees might be destroyed within a few months after being attacked, leads to ...major ecological and financial losses. In this article, we presented a model of pine wilt disease in the trees considering the interaction between nematodes, transmitting beetles with both asymptomatic and symptomatic pine trees. The disease dynamics is first displayed through a schematic diagram which is then transformed to non-linear coupled integer order ODEs through the law of mass action. The positivity, boundedness and equilibrium points has been analyzed and basic reproduction number is calculated through the next generation technique. Sensitivity analysis is also done for the most sensitive parameters which is also displayed through different figures and tables. The solution of the considered nonlinear fractal-fractal model has been obtained through numerical method via MATLAB software. Some numerical results have been obtained and it has been observed that the fractional model give us the more general results by considering different non-integer orders and the integer order results can be easily recovered. It is also noticed that reducing the interaction among the infected beetles and susceptible trees by killing the main source of the infection i.e., killing beetles can reduce the infection drastically, which are briefly discussed and conclusion has been drawn on the basis of the obtained results.
•A mathematical model for the pine wilt disease dynamics is considered.•All the possibilities of interaction of trees and beetles are considered.•Using law of mass action, the physical model is transformed into system of ODEs.•Fractal-Fractional differential operator is applied to integer order ODE system.•Simulation results are obtained by use of a numerical approach.
Mathematical models of in-host viral dynamics and immune response are a vital tool for patient-specific estimation of the initial viral load, prediction of the course of an infection, etc. The ...COVID-19 pandemics has given impetus to the development of models with an ever-increasing degree of complexity. We show that one of the most popular models---the Target Cell Limited model---fails the identifiability test, i.e., its parameters cannot be uniquely inferred from readily available data such as viral load measurements. Here, we present a model that is both identifiable and parsimonious according to information criteria. Our model's predictions match both reported observations of COVID-19 patients and predictions of its more complex counterparts.
We address a mathematical model to approximate in a coarse qualitative the interaction between inbreeding-lobbying and interdisciplinarity in academia and perform a one and two-parameter numerical ...bifurcation analysis to analyse its dynamics. Disciplinary diversity is a necessary condition for the development of interdisciplinarity, which is being recognized today as the key to establish a vibrant academic environment with bigger potential for breakthroughs/innovation in research and technology. However, the interaction of several factors including institutional policies, and behavioural attitudes put significant barriers on advancing interdisciplinarity. A “cognitive rigidity” may rise due to reactive academic lobby behaviours favouring inbreeding. The proposed model consists of four coupled non-linear Ordinary Differential Equations simulating the interaction between certain types of academic behaviour and the rate of knowledge advancement which is related to the level of disciplinary diversity. The effect of a control policy that inhibits inbreeding-lobbying is also investigated. The numerical bifurcation analysis reveals a rich nonlinear behaviour including multistability, sustained oscillations, limit points of limit cycles, homoclinic bifurcations as well as codimension-two bifurcations and in particular Bogdanov–Takens and Bautin bifurcations.
One ring to rule them all Zotti, Maurizio; De Filippis, Francesca; Cesarano, Gaspare ...
New phytologist,
08/2020, Volume:
227, Issue:
3
Journal Article
Peer reviewed
Open access
• Species coexistence in grasslands is regulated by several environmental factors and interactions with the soil microbial community.
• Here, the development of the Basidiomycetes fungus Agaricus ...arvensis, forming fairy rings, in a species-rich Mediterranean grassland, is described. Effects of the mycelial front on plants, fungi and bacteria were assessed by vegetation survey and next generation sequencing approaches.
• Our results showed a fungal-dependent shift in the community structure operated by a wave-like spread of fairy rings that decreased plant, fungal and bacterial diversity, indicating a detrimental effect of fairy rings on most species. The fairy rings induced successional processes in plants that enhanced the replacement of a community dominated by perennial plants with short-living and fast-growing plant species. In parallel, fungal and bacterial communities showed evident differences in species composition with several taxa associated within distinct sampling zone across the fairy rings. Notably, bacteria belonging to the Burkholderia genus and fungi of the genus Trichoderma increased in response to the advancing mycelium of A. arvensis.
• The profound changes in community composition and the overall increase in taxa diversity at ecosystemic scale suggest that fairy ring-forming fungi may act as ecosystem engineer species in Mediterranean grasslands.
We develop a
2
×
2
evolutionary matrix game to model vegetation dynamics due to the effect of autotoxicity. The phenomenon of autotoxicity refers to the rise in soil of negative conditions for plant ...performance induced by the plants themselves. Relating the Nash Equilibrium Strategies of the game to the stability of the equilibrium points of the induced population dynamics, we investigate under which conditions coexistence of low and highly sensitive to autotoxicity plants occurs and under which a monospecific population dominates the competition. Based on this classification, we investigate the optimal distribution of the two distinct types of plants in order to maximize the cumulative total fitness and determine if this distribution is stable. The primary outcome of this study is to analyze the necessary conditions for achieving the highest total fitness in both mixed and monospecific populations of low-sensitivity plants. In contrast, we argue that a monospecific population of highly sensitive plants can never maximize overall fitness.
The problem of supporting decision- and policy-makers in managing issues related to solid waste and water quality was addressed within the context of a participatory modeling framework in the ...Sagarmatha National Park and Buffer Zone in Nepal. We present the main findings of management-oriented research projects conducted within this framework, thus providing an overview of the current situation in the park regarding solid waste and water quality issues. We found that most of the solid waste generated in the park is composed of organic matter, paper, and minor reused waste that is mainly reused for cattle feeding and manure, while disposal of other nondegradable categories of collected waste (glass, metal, and plastic) is not properly managed. Particularly, burning or disposal in open dumps poses a great hazard to environmental, human, and animal health, as most dump sites situated close to water courses are prone to regular flooding during the rainy season, thereby directly contaminating river water. Pollutants and microbiological contamination in water bodies were found and anthropogenic activities and hazardous practices such as solid waste dump sites, open defecation, and poor conditions of existing septic tanks are suggested as possibly affecting water quality. Collection of these data on solid waste and water quality and compilation of management information on the targeted social-ecological system allowed us to develop consensus-building models to be used as management supporting tools. By implementing such models, we were able to simulate scenarios identifying and evaluating possible management solutions and interventions in the park. This work reveals insights into general dynamics that can support the quest for solutions to waste and water quality management problems in other protected areas and mountain landscapes where traditional livelihood and land use patterns are changing under the influence of a growing population, changing consumption patterns, and international tourism.
Spatial patterns and self‐organization of plants has been a subject of fascination because the underlying mechanisms have been hard to determine, raising different explanatory hypotheses. Plant–soil ...negative feedback (PSNF) – defined as the induction of negative conditions for conspecific establishment – has been widely studied in both field and laboratory conditions, and conceptually demonstrated by some modelling works. We present a mechanistic model, integrating individual plants inside an agent‐based framework, to explore the effects of PSNF on the spatial and temporal dynamics of virtual populations and communities of plants of diverse growth forms. This endeavour led to the reproduction of well‐known vegetation patterns observed at various scales, demonstrating for the first time a unified mechanism behind the spatial patterns of Janzen–Connell seedlings’ distribution, ring formation, and the high species mobility in species‐rich grasslands. These results support the ecological relevance of PSNF in the regulation of spatial organization and biodiversity dynamics in plant communities. More specifically, PSNF due to autoxicity seems most coherent with the spatio‐temporal scale of dynamics displayed here.
The emergence and maintenance of tree species diversity in tropical forests is commonly attributed to the Janzen-Connell (JC) hypothesis, which states that growth of seedlings is suppressed in the ...proximity of conspecific adult trees. As a result, a JC distribution due to a density-dependent negative feedback emerges in the form of a (transient) pattern where conspecific seedling density is highest at intermediate distances away from parent trees. Several studies suggest that the required density-dependent feedbacks behind this pattern could result from interactions between trees and soil-borne pathogens. However, negative plant-soil feedback may involve additional mechanisms, including the accumulation of autotoxic compounds generated through tree litter decomposition. An essential task therefore consists in constructing mathematical models incorporating both effects showing the ability to support the emergence of JC distributions. In this work, we develop and analyse a novel reaction-diffusion-ODE model, describing the interactions within tropical tree species across different life stages (seeds, seedlings, and adults) as driven by negative plant-soil feedback. In particular, we show that under strong negative plant-soil feedback travelling wave solutions exist, creating transient distributions of adult trees and seedlings that are in agreement with the Janzen-Connell hypothesis. Moreover, we show that these travelling wave solutions are pulled fronts and a robust feature as they occur over a broad parameter range. Finally, we calculate their linear spreading speed and show its (in)dependence on relevant nondimensional parameters.
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