Md
M.N. de Jong
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This dissertation contributes to the intersection of biological and ecological modelling on the one hand, and systems and control theory on the other. It examines domain-specific problems from the biomedical and agricultural sectors through a dynamic systems and control perspective. In each case study, we develop or adopt a mathematical model to describe the system dynamics and incorporate suitable control inputs. After analysing these models to establish key properties such as positivity, boundedness, and realistic asymptotic behaviour, we formulate practical management problems ranging from antiviral treatment planning to agricultural scheduling as optimal control problems. These formulations jointly capture economic objectives and the biological or ecological responses to inputs.
As a first contribution, we develop a novel differential equation model of mpox virus infection that captures the distinct effects of two candidate antiviral drugs. We analyse the model to understand its behaviour and apply optimal control to design multi-drug treatment strategies that minimise both viral load and drug use.
Next, in the first agricultural case study, we use a discrete-time annual weed population model with crop sowing densities as control inputs to investigate sustainable and economically optimal weed management. We establish global stability of periodic state trajectories and formulate the problem as a periodic optimal control problem, yielding sustainable solutions that maximise long-run economic profit. We then extend this principle to a broader class of systems, including weeds, disease, and soil nutrient dynamics. We introduce a transient optimisation framework based on finite-horizon optimal control with a terminal value function derived from periodic reference solutions and their convergence properties. This terminal value function enables the resulting solutions to achieve infinite-horizon performance that matches or exceeds that of periodic and myopic approaches, making them both sustainable and responsive to initial conditions. We demonstrate the methodology using various agricultural models and optimisation problems from the literature, illustrating its implementation and confirming the theoretical guarantees.
Finally, we address within-season optimal crop scheduling. We model crop growth in an intercropping system using a competitive Lotka-Volterra framework and estimate parameters from published time series data of oat and lupin in isolation, monocultures, and bicultures. We incorporate sowing and harvesting as impulsive control actions that reset biomasses and plant densities, and discretise this impulsive control system for optimal control. Unlike conventional steady-state approaches, this framework enables the optimisation of relay intercropping and produces substantially higher economic yields.
Collectively, these contributions demonstrate how systems and control theory can provide new analytical insights, theoretical guarantees, and flexible optimisation strategies for biological and ecological management, offering advanced solutions that go beyond conventional steady-state and myopic approaches. ...
As a first contribution, we develop a novel differential equation model of mpox virus infection that captures the distinct effects of two candidate antiviral drugs. We analyse the model to understand its behaviour and apply optimal control to design multi-drug treatment strategies that minimise both viral load and drug use.
Next, in the first agricultural case study, we use a discrete-time annual weed population model with crop sowing densities as control inputs to investigate sustainable and economically optimal weed management. We establish global stability of periodic state trajectories and formulate the problem as a periodic optimal control problem, yielding sustainable solutions that maximise long-run economic profit. We then extend this principle to a broader class of systems, including weeds, disease, and soil nutrient dynamics. We introduce a transient optimisation framework based on finite-horizon optimal control with a terminal value function derived from periodic reference solutions and their convergence properties. This terminal value function enables the resulting solutions to achieve infinite-horizon performance that matches or exceeds that of periodic and myopic approaches, making them both sustainable and responsive to initial conditions. We demonstrate the methodology using various agricultural models and optimisation problems from the literature, illustrating its implementation and confirming the theoretical guarantees.
Finally, we address within-season optimal crop scheduling. We model crop growth in an intercropping system using a competitive Lotka-Volterra framework and estimate parameters from published time series data of oat and lupin in isolation, monocultures, and bicultures. We incorporate sowing and harvesting as impulsive control actions that reset biomasses and plant densities, and discretise this impulsive control system for optimal control. Unlike conventional steady-state approaches, this framework enables the optimisation of relay intercropping and produces substantially higher economic yields.
Collectively, these contributions demonstrate how systems and control theory can provide new analytical insights, theoretical guarantees, and flexible optimisation strategies for biological and ecological management, offering advanced solutions that go beyond conventional steady-state and myopic approaches. ...
This dissertation contributes to the intersection of biological and ecological modelling on the one hand, and systems and control theory on the other. It examines domain-specific problems from the biomedical and agricultural sectors through a dynamic systems and control perspective. In each case study, we develop or adopt a mathematical model to describe the system dynamics and incorporate suitable control inputs. After analysing these models to establish key properties such as positivity, boundedness, and realistic asymptotic behaviour, we formulate practical management problems ranging from antiviral treatment planning to agricultural scheduling as optimal control problems. These formulations jointly capture economic objectives and the biological or ecological responses to inputs.
As a first contribution, we develop a novel differential equation model of mpox virus infection that captures the distinct effects of two candidate antiviral drugs. We analyse the model to understand its behaviour and apply optimal control to design multi-drug treatment strategies that minimise both viral load and drug use.
Next, in the first agricultural case study, we use a discrete-time annual weed population model with crop sowing densities as control inputs to investigate sustainable and economically optimal weed management. We establish global stability of periodic state trajectories and formulate the problem as a periodic optimal control problem, yielding sustainable solutions that maximise long-run economic profit. We then extend this principle to a broader class of systems, including weeds, disease, and soil nutrient dynamics. We introduce a transient optimisation framework based on finite-horizon optimal control with a terminal value function derived from periodic reference solutions and their convergence properties. This terminal value function enables the resulting solutions to achieve infinite-horizon performance that matches or exceeds that of periodic and myopic approaches, making them both sustainable and responsive to initial conditions. We demonstrate the methodology using various agricultural models and optimisation problems from the literature, illustrating its implementation and confirming the theoretical guarantees.
Finally, we address within-season optimal crop scheduling. We model crop growth in an intercropping system using a competitive Lotka-Volterra framework and estimate parameters from published time series data of oat and lupin in isolation, monocultures, and bicultures. We incorporate sowing and harvesting as impulsive control actions that reset biomasses and plant densities, and discretise this impulsive control system for optimal control. Unlike conventional steady-state approaches, this framework enables the optimisation of relay intercropping and produces substantially higher economic yields.
Collectively, these contributions demonstrate how systems and control theory can provide new analytical insights, theoretical guarantees, and flexible optimisation strategies for biological and ecological management, offering advanced solutions that go beyond conventional steady-state and myopic approaches.
As a first contribution, we develop a novel differential equation model of mpox virus infection that captures the distinct effects of two candidate antiviral drugs. We analyse the model to understand its behaviour and apply optimal control to design multi-drug treatment strategies that minimise both viral load and drug use.
Next, in the first agricultural case study, we use a discrete-time annual weed population model with crop sowing densities as control inputs to investigate sustainable and economically optimal weed management. We establish global stability of periodic state trajectories and formulate the problem as a periodic optimal control problem, yielding sustainable solutions that maximise long-run economic profit. We then extend this principle to a broader class of systems, including weeds, disease, and soil nutrient dynamics. We introduce a transient optimisation framework based on finite-horizon optimal control with a terminal value function derived from periodic reference solutions and their convergence properties. This terminal value function enables the resulting solutions to achieve infinite-horizon performance that matches or exceeds that of periodic and myopic approaches, making them both sustainable and responsive to initial conditions. We demonstrate the methodology using various agricultural models and optimisation problems from the literature, illustrating its implementation and confirming the theoretical guarantees.
Finally, we address within-season optimal crop scheduling. We model crop growth in an intercropping system using a competitive Lotka-Volterra framework and estimate parameters from published time series data of oat and lupin in isolation, monocultures, and bicultures. We incorporate sowing and harvesting as impulsive control actions that reset biomasses and plant densities, and discretise this impulsive control system for optimal control. Unlike conventional steady-state approaches, this framework enables the optimisation of relay intercropping and produces substantially higher economic yields.
Collectively, these contributions demonstrate how systems and control theory can provide new analytical insights, theoretical guarantees, and flexible optimisation strategies for biological and ecological management, offering advanced solutions that go beyond conventional steady-state and myopic approaches.
Agricultural production of annual crops is often hampered by annual weeds, which compete with planted crops and persist through the collection of dormant seeds in the soil called the weed seed bank. Conventional weed management relies heavily on chemical herbicides, which are not sustainable. A complementary method that reduces the need for herbicides is ‘cultural control’, in which the crop rotation is designed in part to manage the weed population. We propose a methodology that optimizes the crop rotation, here defined as periodic crop planting densities, subject to periodic weed dynamics. We adopt a well-established model of discrete-time annual weed seed bank dynamics with crop planting density inputs, and show that any periodic weed seed bank trajectory corresponding to a periodic crop rotation is globally exponentially stable. This guarantees convergence to the optimal periodic trajectory obtained by solving a nonlinear optimal control problem with periodic constraints, which we formulate as a nonlinear program.
...
Agricultural production of annual crops is often hampered by annual weeds, which compete with planted crops and persist through the collection of dormant seeds in the soil called the weed seed bank. Conventional weed management relies heavily on chemical herbicides, which are not sustainable. A complementary method that reduces the need for herbicides is ‘cultural control’, in which the crop rotation is designed in part to manage the weed population. We propose a methodology that optimizes the crop rotation, here defined as periodic crop planting densities, subject to periodic weed dynamics. We adopt a well-established model of discrete-time annual weed seed bank dynamics with crop planting density inputs, and show that any periodic weed seed bank trajectory corresponding to a periodic crop rotation is globally exponentially stable. This guarantees convergence to the optimal periodic trajectory obtained by solving a nonlinear optimal control problem with periodic constraints, which we formulate as a nonlinear program.
Journal article
(2023)
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Maarten de Jong, Francesca Cala Campana, Pengfei Li, Qiuwei Pan, Giulia Giordano
In 2022, worldwide mpox outbreaks have called attention to mpox virus infection and treatment opportunities using the drugs cidofovir and tecovirimat, which target different stages of in-host viral proliferation, respectively production and shedding. We propose a new model of in-host viral infection dynamics that distinguishes between the two stages, so as to explore the distinct effects of the two drugs, and we analyse the model properties and behaviour. Reducing the model order via timescale separation is shown to lead to the classical target-cell limited model, with a lumped viral proliferation rate depending on both production and shedding. We explicitly introduce the effect of the two drugs and we exemplify how to formulate and solve an optimal control problem that leverages the model dynamics to schedule optimal combined treatments.
...
In 2022, worldwide mpox outbreaks have called attention to mpox virus infection and treatment opportunities using the drugs cidofovir and tecovirimat, which target different stages of in-host viral proliferation, respectively production and shedding. We propose a new model of in-host viral infection dynamics that distinguishes between the two stages, so as to explore the distinct effects of the two drugs, and we analyse the model properties and behaviour. Reducing the model order via timescale separation is shown to lead to the classical target-cell limited model, with a lumped viral proliferation rate depending on both production and shedding. We explicitly introduce the effect of the two drugs and we exemplify how to formulate and solve an optimal control problem that leverages the model dynamics to schedule optimal combined treatments.