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We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a…
The influence of competition and additional food on prey-predator dynamics has attracted considerable interest from mathematical biology researchers in recent times. In this study, we consider an additional food provided prey-predator model…
We consider an additional food provided prey-predator model exhibiting Holling type IV functional response with combined continuous white noise and discontinuous L\'evy noise. We prove the existence and uniqueness of global positive…
This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. A biological prey-predator model is also analyzed with a modification function growth in prey…
The dynamics of predator-prey systems influenced by intra-specific competition and additional food resources have increasingly become a subject of rigorous study in the realm of mathematical biology. In this study, we consider an additional…
The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…
Vector/Pest control is essential to reduce the risk of vector-borne diseases or losses in crop fields. Among biological control tools, the sterile insect technique (SIT), is the most promising one. SIT control generally consists of massive…
Agricultural losses to pest represent an important challenge in a global warming scenario. Intercropping is an alternative farming practice that promotes pest control without the use of chemical pesticides. Here we develop a mathematical…
In the prospect of ecology and biology, studying insect-plant predation will considerably contribute to pest control, benefit agriculture and afforestation, and also help people to better understand insect-plant co-evolution. Therefore, we…
In the natural world, there are many insect species whose individual members have a life history that takes them through two stages, immature and mature. Moreover, the rates of survival, development, and reproduction almost always depend on…
Elucidating the fitness measures optimized during the evolution of complex biological systems is a major challenge in evolutionary theory. We present experimental evidence and an analytical framework demonstrating how biochemical networks…
Biological control, the use of predators and pathogens to control target pests, is a promising alternative to chemical control. It is hypothesized that the introduced predators efficacy can be boosted by providing them with an additional…
Biological pest control is increasingly used in agriculture as a an alternative to traditional chemical pest control. In many cases, this involves a one-off or periodic release of naturally occurring and/or genetically modified enemies such…
Optimal control of large particle systems with collective dynamics by few agents is a subject of high practical importance (e.g. in evacuation dynamics), but still limited mathematical basis. In particular the transition from discrete…
We consider a nonautonomous eco-epidemiological model with general functions for predation on infected and uninfected preys as well as general functions associated to the vital dynamics of the susceptible prey and predator populations. We…
Disease and pest control largely rely on pesticides use and progress still remains to be made towards more sustainable practices. Pest Monitoring Networks (PMNs) can provide useful information for improving crop protection by restricting…
We derive the explicit solutions to singular stochastic control problems of the monotone follower type with (a) an expected discounted criterion, (b) an expected ergodic criterion and (c) a pathwise ergodic criterion. These problems have…
This paper is concerned with existence, non-existence and uniqueness of positive (coexistence) steady states to a predator-prey system with density-dependent dispersal. To overcome the analytical obstacle caused by the cross-diffusion…
Ecology and evolution are inseparable. Motivated by some recent experiments, we have developed models of evolutionary ecology from the perspective of dynamic networks. In these models, in addition to the intra-node dynamics, which…
In this paper, we explore the solvability and the optimal control problem for a compartmental model based on reaction-diffusion partial differential equations describing a transmissible disease. The nonlinear model takes into account the…