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Ontogenic resistance has been described for many plant-pathogen systems. Conversely, coffee leaf rust, a major fungal disease that drastically reduces coffee production, exhibits a form of ontogenic susceptibility, with a higher infection risk for mature leaves. To take into account stage-dependent crop response to phytopathogenic fungi, we developed an SEIR-U epidemiological model, where U stands for spores, which differentiates between young and mature leaves. Based on this model, we also explored the impact of ontogenic resistance on the sporulation rate. We computed the basic reproduction number R 0 , which classically determines the stability of the disease-free equilibrium. We identified forward and backward bifurcation cases. The backward bifurcation is generated by the high sporulation of young leaves compared to mature ones. In this case, when the basic reproduction number is less than one, the disease can persist. These results provide useful insights on the disease dynamics and its control. In particular, ontogenic resistance may require higher control efforts to eradicate the disease. [ABSTRACT FROM AUTHOR]

Growing genetically resistant plants allows pathogen populations to be controlled and reduces the use of pesticides. However, pathogens can quickly overcome such resistance. In this context, how can we achieve sustainable crop protection? This crucial question has remained largely unanswered despite decades of intense debate and research effort. In this study, we used a bibliographic analysis to show that the research field of resistance durability has evolved into three subfields: (1) "plant breeding" (generating new genetic material), (2) "molecular interactions" (exploring the molecular dialogue governing plant–pathogen interactions) and (3) "epidemiology and evolution" (explaining and forecasting of pathogen population dynamics resulting from selection pressure[s] exerted by resistant plants). We argue that this triple split of the field impedes integrated research progress and ultimately compromises the sustainable management of genetic resistance. After identifying a gap among the three subfields, we argue that the theoretical framework of population genetics could bridge this gap. Indeed, population genetics formally explains the evolution of all heritable traits, and allows genetic changes to be tracked along with variation in population dynamics. This provides an integrated view of pathogen adaptation, in particular via evolutionary–epidemiological feedbacks. In this Opinion Note, we detail examples illustrating how such a framework can better inform best practices for developing and managing genetically resistant cultivars. [ABSTRACT FROM AUTHOR]

The coffee berry borer (CBB), Hypothenemus hampei, is the most destructive insect pest affecting coffee plantations in most coffee-producing countries, hence causing major economic losses worldwide. The cryptic life cycle of CBB inside coffee berries makes their control extremely difficult. To tackle this problem, we use a dynamical model describing the plant–pest interactions during a cropping season, which includes a berry age structure to account for CBB preference for mature berries. We introduce two environmentally friendly control methods, consisting in applying a bio-insecticide to reduce berry infestation and in trapping the colonising CBB. Our objective is to maximise the profit generated by the harvest of healthy coffee berries, while minimising the CBB population for the next cropping season. The existence of an optimal control strategy is provided, and necessary optimality conditions are established. Finally, the optimal control problem is solved numerically and simulations are provided. They show that combining the two control methods is a cost-effective strategy to protect coffee berries from CBB infestation. [ABSTRACT FROM AUTHOR]

Coffee berry borer Hypothenemus hampei (Coleoptera: Scolytidae), denoted CBB, is the most important insect pest of coffee worldwide, with a high impact on the economy of coffee producing countries. The insect spends a great part of its life cycle inside the coffee berry and causes severe crop losses. Biological control based on the use of an entomopathogenic fungus is a major alternative to chemical pesticides in order to control CBB. The fungus is sprayed on the coffee berries to kill CBB when the insects drill holes to penetrate inside the berries. Our aim in this work is to optimise the fungus application, using a modelling approach. We first formulate a mathematical model describing the infestation dynamics of coffee berries by CBB. We analyse the model and show that the stability of the pest‐free and coexistence equilibria depends on the basic reproduction number. To introduce a control variable corresponding to the application of an entomopathogenic fungus, we then extend the model and include the fungus dynamics. We formulate an optimal problem which consists in maximising the coffee yield, while minimising the control cost, as well as the CBB population for the next cropping season. The existence of the optimal control and the necessary optimality condition are established using Pontryagin's Maximum Principle. The optimal control problem is solved numerically using the BOCOP software and simulations are provided, showing that the use of entomopathogenic fungus effectively controls CBB. [ABSTRACT FROM AUTHOR]

Marine viruses interact with microbial hosts in dynamic environments shaped by variation in abiotic factors, including temperature. However, the impacts of temperature on viral infection of phytoplankton are not well understood. Here we coupled mathematical modelling with experiments to explore the effect of temperature on virus‐phytoplankton interactions. Our model shows the negative consequences of high temperatures on infection and suggests a temperature‐dependent threshold between viral production and degradation. Modelling long‐term dynamics in environments with different average temperatures revealed the potential for long‐term host‐virus coexistence, epidemic free or habitat loss states. We generalised our model to variation in global sea surface temperatures corresponding to present and future seas and show that climate change may differentially influence virus‐host dynamics depending on the virus‐host pair. Temperature‐dependent changes in the infectivity of virus particles may lead to shifts in virus‐host habitats in warmer oceans, analogous to projected changes in the habitats of macro‐, microorganisms and pathogens. [ABSTRACT FROM AUTHOR]

Coffee leaf rust (CLR) is one of the main diseases that affect coffee plantations worldwide. It is caused by the fungus Hemileia vastatrix. Damages induce severe yield losses (up to 70%). Its control mainly relies on cultural practices and fungicides, the latter having harmful ecological impact and important cost. Our goal is to understand the propagation of this fungus in order to propose a biocontrol solution, based on a mycoparasite that inhibits H. vastatrix reproduction. We develop and explore a spatio-temporal model that describes CLR propagation in a coffee plantation during the rainy and dry seasons. We show the existence of a solution and prove that there exists two threshold parameters, the dry and rainy basic reproduction numbers, that determine the stability of the equilibria for the dry and rainy season subsystems. To illustrate these theoretical results, numerical simulations are performed, using a non-standard finite method to integrate the pest model. We also numerically investigate the biocontrol impact. We determine its efficiency threshold in order to ensure CLR eradication. [ABSTRACT FROM AUTHOR]

Root‐knot nematodes, Meloidogyne spp., are soil‐borne polyphagous pests with major impact on crop yield worldwide. Resistant crops efficiently control avirulent root‐knot nematodes, but favour the emergence of virulent forms. Since virulence is associated with fitness costs, susceptible crops counter‐select virulent root‐knot nematodes. In this study, we identify optimal rotation strategies between susceptible and resistant crops to control root‐knot nematodes and maximize crop yield. We developed an epidemiological model describing the within‐season dynamics of avirulent and virulent root‐knot nematodes on susceptible or resistant plant root‐systems, and their between‐season survival. The model was fitted to experimental data and used to predict yield‐maximizing rotation strategies, with special attention to the impact of epidemic severity and genetic parameters. Crop rotations were found to be efficient under realistic parameter ranges. They were characterized by low ratios of resistant plants and were robust to parameter uncertainty. Rotations provide significant gain over resistant‐only strategies, especially under intermediate fitness costs and severe epidemic contexts. Switching from the current general deployment of resistant crops to custom rotation strategies could not only maintain or increase crop yield, but also preserve the few and valuable R‐genes available. [ABSTRACT FROM AUTHOR]

Background: Understanding what determines the between-host variability in infection dynamics is a key issue to better control the infection spread. In particular, pathogen clearance is desirable over rebounds for the health of the infected individual and its contact group. In this context, the Porcine Respiratory and Reproductive Syndrome virus (PRRSv) is of particular interest. Numerous studies have shown that pigs similarly infected with this highly ubiquitous virus elicit diverse response profiles. Whilst some manage to clear the virus within a few weeks, others experience prolonged infection with a rebound. Despite much speculation, the underlying mechanisms responsible for this undesirable rebound phenomenon remain unclear. Results: We aimed at identifying immune mechanisms that can reproduce and explain the rebound patterns observed in PRRSv infection using a mathematical modelling approach of the within-host dynamics. As diverse mechanisms were found to influence PRRSv infection, we established a model that details the major mechanisms and their regulations at the between-cell scale. We developed an ABC-like optimisation method to fit our model to an extensive set of experimental data, consisting of non-rebounder and rebounder viremia profiles. We compared, between both profiles, the estimated parameter values, the resulting immune dynamics and the efficacies of the underlying immune mechanisms. Exploring the influence of these mechanisms, we showed that rebound was promoted by high apoptosis, high cell infection and low cytolysis by Cytotoxic T Lymphocytes, while increasing neutralisation was very efficient to prevent rebounds. Conclusions: Our paper provides an original model of the immune response and an appropriate systematic fitting method, whose interest extends beyond PRRS infection. It gives the first mechanistic explanation for emergence of rebounds during PRRSv infection. Moreover, results suggest that vaccines or genetic selection promoting strong neutralising and cytolytic responses, ideally associated with low apoptotic activity and cell permissiveness, would prevent rebound. [ABSTRACT FROM AUTHOR]

The immune mechanisms which determine the infection duration induced by pathogens targeting pulmonary macrophages are poorly known. To explore the impact of such pathogens, it is indispensable to integrate the various immune mechanisms and to take into account the variability in pathogen virulence and host susceptibility. In this context, mathematical models complement experimentation and are powerful tools to represent and explore the complex mechanisms involved in the infection and immune dynamics. We developed an original mathematical model in which we detailed the interactions between the macrophages and the pathogen, the orientation of the adaptive response and the cytokine regulations. We applied our model to the Porcine Respiratory and Reproductive Syndrome virus (PRRSv), a major concern for the swine industry. We extracted value ranges for the model parameters from modelling and experimental studies on respiratory pathogens. We identified the most influential parameters through a sensitivity analysis. We defined a parameter set, the reference scenario, resulting in a realistic and representative immune response to PRRSv infection. We then defined scenarios corresponding to graduated levels of strain virulence and host susceptibility around the reference scenario. We observed that high levels of antiviral cytokines and a dominant cellular response were associated with either short, the usual assumption, or long infection durations, depending on the immune mechanisms involved. To identify these mechanisms, we need to combine the levels of antiviral cytokines, including , and . The latter is a good indicator of the infected macrophage level, both combined provide the adaptive response orientation. Available PRRSv vaccines lack efficiency. By integrating the main interactions between the complex immune mechanisms, this modelling framework could be used to help designing more efficient vaccination strategies. [ABSTRACT FROM AUTHOR]

Presents a study that examined the regulation of a fishery using a bioeconomics model. Features of the model; Details of the regulation process; Comparison between a local optimal control resolution approach and an invariant dominant approach for fishery regulation.

The framework of this article is modeling applied to fisheries. It aims at relating some classical stock–recruitment curves to a dynamic structured model, consisting of the adults stages of the stock and a pre-recruits stage (i.e., eggs, larvae, juveniles). The main result is that no functional stock–recruitment relationship can be found, unless further restrictive assumptions are added to the model (slow–fast dynamics and uniformity). Among the curves thus obtained is the Beverton–Holt curve, but not Ricker's. [ABSTRACT FROM AUTHOR]

Background: Understanding the dynamical behaviour of biological systems is challenged by their large number of components and interactions. While efforts have been made in this direction to reduce model complexity, they often prove insufficient to grasp which and when model processes play a crucial role. Answering these questions is fundamental to unravel the functioning of living organisms. Results: We design a method for dealing with model complexity, based on the analysis of dynamical models by means of Principal Process Analysis. We apply the method to a well-known model of circadian rhythms in mammals. The knowledge of the system trajectories allows us to decompose the system dynamics into processes that are active or inactive with respect to a certain threshold value. Process activities are graphically represented by Boolean and Dynamical Process Maps. We detect model processes that are always inactive, or inactive on some time interval. Eliminating these processes reduces the complex dynamics of the original model to the much simpler dynamics of the core processes, in a succession of sub-models that are easier to analyse. We quantify by means of global relative errors the extent to which the simplified models reproduce the main features of the original system dynamics and apply global sensitivity analysis to test the influence of model parameters on the errors. Conclusion: The results obtained prove the robustness of the method. The analysis of the sub-model dynamics allows us to identify the source of circadian oscillations. We find that the negative feedback loop involving proteins PER, CRY, CLOCK-BMAL1 is the main oscillator, in agreement with previous modelling and experimental studies. In conclusion, Principal Process Analysis is a simple-to-use method, which constitutes an additional and useful tool for analysing the complex dynamical behaviour of biological systems. [ABSTRACT FROM AUTHOR]