The sterile insect technique (SIT) is a pest control strategy based on the mass release of sterilized males to disrupt natural reproduction and suppress wild populations. However, its effectiveness can be challenged by biological factors such as female multiple mating and sperm use bias. While multiple mating is widespread among many insect species, the mechanisms governing sperm use remain poorly understood. In this study, we develop and analyze a compartmental mathematical model based on differential equations to investigate the overall impact of multiple mating on SIT efficiency. We further analyze the effect of sperm use biases with an agent-based model, calibrated on Drosophila suzukii, allowing the exploration of different scenarios: preferential use of first vs last sperm, of fertile vs sterile sperm, and mixed sperm use. Our results highlight how multiple mating and sperm use biases influence SIT effectiveness. In the longer term, multiple mating is disadvantageous as it requires additional releases of sterilized males to control the pest population. However, in the shorter term, it can be beneficial by disrupting further female reproductive output by "defertilizing" females mated with wild males. This study provides new information on how the way sperm is processed after mating can impact sterile insect control strategies, highlighting the limited influence of these biological processes depending on the release efforts that can be deployed.

Building upon the ODE model describing the dynamics of healthy and leukemic cells introduced in Kumar et al. (2024); Stiehl and Marciniak-Czochra (2012), we propose an extended framework that incorporates a control variable representing the effects of chemotherapy. This extension aims to provide a more refined mathematical basis for investigating anti-cancer strategies. First, we perform a stability analysis of the equilibria associated with healthy and leukemic states, partly estimated from clinical data. This analysis reveals a complex structure, including the emergence of a continuum of coexistence states and bifurcation thresholds that play a key role in the subsequent optimization stage. Based on these findings, we investigate an optimal control problem to minimize leukemia stem cells while limiting drug toxicity. Pontryagin’s Maximum Principle provides necessary conditions for optimality, and direct numerical optimization confirms the predicted structures, motivating the study of the static problem. This static formulation reveals an unconventional feature: the cost functional becomes set-valued due to the continuum of equilibria, placing the problem outside the scope of standard methods. Simulations reveal a turnpike phenomenon, where over long time horizons the dynamic trajectories closely approximate the ideal static structure. Finally, a sensitivity analysis of the performance criterion with respect to key parameters complements the study, providing preliminary insights into which biological mechanisms may influence the optimal therapeutic outcomes. We conclude with a discussion of these findings.

Banana and plantain production is severely threatened by Radopholus similis, a parasitic nematode that lives and propagates within plant roots, causing substantial damage and making effective control particularly challenging. Building on a recently introduced and analyzed model, we upgrade the framework to account for the combined effect of two biological control levers against Radopholus similis: a biostimulant effort reducing infestation rate, and a biopesticide effort directly lowering nematode density. To investigate the most effective biocontrol strategies, we formulate an optimal control problem and derive first-order necessary conditions using Pontryagin’s Maximum Principle. The problem is solved numerically via direct methods using Bocop, yielding bang-bang-type solutions where the two controls are activated in a quasi-alternating pattern. We further compare this optimal strategy with a structured periodic control policy, showing that it provides close performance with simpler implementation.

Plant-parasitic nematodes are responsible for significant economic losses worldwide, affecting a wide range of crops. They infect and divert resources and impair plant growth. While resistance aims to limit parasite burden, tolerance is the ability of a plant to maintain its yield despite infection, which offers a complementary and potentially more sustainable strategy. Understanding how tolerance arises and operates requires mechanistic insights into host-parasite interactions and the constraints that shape them. In this study, we develop a mathematical model describing the coupled dynamics of plant growth, internal resource allocation, and nematode population processes. The model incorporates key biological mechanisms, including resource-dependent plant development, nematode infection, reproduction and feedbacks between resource limitation and parasitism. We analytically derive the basic reproduction number and identify equilibrium states, including the system extinction, healthy plantation and coexistence. Our analysis shows that coexistence strongly depends on plant resource production, shedding light on conditions under which tolerance can emerge. Numerical simulations further explore how variations in both plant and nematode parameters influence the tolerance over a cropping season. We highlight the dual role of resource production: high production rates not only boost plant growth but also enhance nematode proliferation. There is hence a compromise to be found between favouring bigger and more productive plants, versus limiting yield losses in case of nematode infestation. This compromise is shaped by the nematode virulence and plant quantitative resistance.

Foragers exploiting heterogeneous habitats make strategic movement decisions to maximize fitness. Charnov's marginal value theorem (MVT) models the sequential visit of habitat patches and their distribution to predict the optimal time allocation strategy. However, it notoriously ignores the effects of predation risk. Brown's giving-up density (GUD) theory is an alternative that includes predation risk. However, it is more abstract and does not have the specificity or graphical appeal of the MVT. Here, we formally introduce the rMVT (r stands for risk), a generalization of the MVT that incorporates predation risks. The rMVT retains the structure and graphical simplicity of the MVT, but implies a shift from residence time to expected dose of risk (micromorts) as the domain over which rate maximization occurs. We show that the rMVT can handle most types of risk, whereas the GUD theory is valid only for specific forms of risk. Applications of the rMVT show that different types of risk can yield opposite responses of optimal strategies to an increase in the risk level, and predict differential behavioral responses observed in experimental vs. natural conditions. The rMVT also predicts the optimal level of risk-taking, or "optimal boldness," and suggests that individuals should generally be bolder in riskier habitats.

The sterile insect technique (SIT) is a biological control technique based on mass-rearing, radiation-based sterilization that can induce fitness costs, and releases of the pest species targeted for population control. Sterile matings, between females and sterilized males, can reduce the overall population growth rate and cause a fall in population density. However, a proportion of irradiated males may escape sterilization, resulting in what is called residual fertility. Our aim in this study was to examine the impact of residual fertility on pest control employing a modeling approach. We modeled pest population dynamics with three generic differential equations representing sterilized males, wild males and wild females. We explored the impact of residual fertility, in the presence or absence of fitness costs, on potential pest control outcomes using a scenario with 100 % male sterilization as our standard of reference. We carried out a detailed mathematical analysis of the model's dynamics by calculating model equilibria and the latter's stability. Bifurcation analyses were performed with parameters for the Mediterranean fruit fly Ceratitis capitata. We showed that, when residual fertility is below a threshold value, wild populations can be eradicated by flooding the landscape with irradiated males. This threshold is higher when residual fertility is associated with fitness costs. Too high a level of residual fertility makes SIT less effective and hinders population eradication. That said, substantial decreases in population density can be achieved even when residual fertility is much larger than the above threshold.

Smallholder farmers rely on their farm earnings to cover operating costs and generate income. That is not an easy task because of the pests, which reduce yields and generate plant protection costs. The farm yield and plant protection depend on the budget capacity of the farmer. In this work, we want to explore conditions for a sustainable and self-financing cabbage farm. We propose then a non-linear mathematical model for cabbage crops by considering the current account of the plantation as a dynamic variable. We assume that this variable increases due to the sale of cabbages, and provides for the seedling purchase, the plant protection costs, and the grower's income. In the first part, we analyze the model without pest management. We determine how the budget must be spent and we show the existence of a double transcritical bifurcation. We quantify the seasonal yield and income, and estimate the damage due to pest herbivory. In the second part, we analyze a slightly simplified version of our model and obtain the existence of a backward bifurcation. Furthermore, we show that botanical pesticides can be used to prevent pest spread with relatively low plant protection costs.

The coffee berry borer (CBB) Hypothenemus hampei (Coleoptera: Scolytidae) is the most important insect pest affecting coffee production worldwide and generating huge economic losses. As most of its life cycle occurs inside the coffee berry, its control is extremely difficult. To tackle this issue, we solve an optimal control problem based on a berry age-structured dynamical model that describes the infestation dynamics of coffee berries by CBB during a cropping season. This problem consists in applying a bio-insecticide at discrete times in order to maximise the economic profit of healthy coffee berries, while minimising the CBB population for the next cropping season. We derive analytically the first-order necessary optimality conditions of the control problem. Numerical simulations are provided to illustrate the effectiveness of the optimal control strategy.

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.

We present a simple mathematical model of ordinary differential equations that describes the interaction between a healthy cell population and cancerous cell population. This model includes the effects on cell populations of chemotherapy and targeted therapy, which are two bounded control variables. We study this model and seek to optimize the fraction of healthy cells within the total cell population over a given therapy period. We apply the Pontryagin Maximum Principle (PMP) and establish the expressions of singular solutions in different interaction cases between healthy and cancer cells. Then, we use a direct optimization method to validate and illustrate our theoretical results.

Current agricultural practices facilitate emergence and spread of plant diseases through the wide use of monocultures. Host mixtures are a promising alternative for sustainable plant disease control. Their effectiveness can be partly explained by priming-induced cross-protection among plants. Priming occurs when plants are challenged with non-infective pathogen genotypes, resulting in increased resistance to subsequent infections by infective pathogen genotypes. We developed an epidemiological model to explore how mixing two distinct resistant varieties can reduce disease prevalence. We considered a pathogen population composed of three genotypes infecting either one or both varieties. We found that host mixtures should not contain an equal proportion of resistant plants, but a biased ratio (e.g. 80 : 20) to minimize disease prevalence. Counter-intuitively, the optimal ratio of resistant varieties should contain a lower proportion of the costliest resistance for the pathogen to break. This benefit is amplified by priming. This strategy also prevents the invasion of pathogens breaking all resistances.

A bstract Foragers exploiting heterogeneous habitats must make strategic movement decisions in order to maximize fitness. Foraging theory has produced very general formalizations of the optimal patch-leaving decisions rational individuals should make. One is Charnov’s Marginal Value Theorem (MVT), which models the sequential visit of habitat patches and their spatial distribution. The MVT has a simple intuitive graphical interpretation in terms of gain functions and travel times. However, it considers only energy gains, and the effect of predation risk on the time allocation strategy is notoriously lacking. An important development that includes predation risk was Brown’s economic treatment of optimal patch leaving decisions, the basis of giving-up density (GUD) theory, often cited as an extension of the MVT. However, it is a more abstract result that does not have the specificities or graphical appeal of the MVT. Although both successful, the two theories are cited by distinct communities and are seldom connected in texbooks. Here we formally introduce the risk-MVT (rMVT), a generalization of the MVT that can incorporate most types of predation risks. We show that Brown’s GUD-theory is equivalent to a rMVT, but applies for one type of predation risk only. The rMVT retains the structure and graphical simplicity of the MVT, but implies a shift from residence time to expected dose of risk (micromort units, as used in decision analysis) as the domain over which rates of gain are computed and maximized. Applications of the rMVT show that different types of risk can yield opposite responses of optimal strategies to an increase in the risk level, and predict differential responses of behaviours observed in experimental versus natural conditions. The risk-MVT can also be used to predict the optimal level of risk taking, or “optimal boldness”, and suggests that individuals should generally be bolder in riskier habitats.

Fungal diseases cause serious damages in crop worldwide. In particular, coffee leaf rust (CLR), caused by fungus Hemileia vastatrix attacks coffee leaves and reduces coffee yield. This paper presents a multi-seasonal model of the CLR development in the coffee plantation with continuous dynamics during the rainy season and a discrete event to represent the simpler dynamics during the dry season. Biological control using predators through one or more discrete introduction events over the year is then added. Analytical and semi-numerical studies are performed to identify how much and how frequently predators need to be introduced through the definition of a threshold value, as a function of various parameters. We show that the best strategy to efficiently control the disease depends on the predator mortality: low mortality parasites need be released only once a year, while high mortality parasites should be released more frequently to ensure their persistence in the plantation. This work hence provides qualitative and quantitative bases for the deployment of predator-based biocontrol, a promising alternative to fungicides for rust control.

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.