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Antimicrobial resistance is one of the biggest threats to global health, food security, and development. Antibiotic overuse and misuse are the main drivers for the emergence of resistance. Studies in the medical sphere have indicated that shortened antibiotic treatments can be as effective as standard fixed-dose ones and have shown that an initial higher dose followed by a lower maintenance dose are more beneficial to patients with critical illnesses. It is crucial to optimise the use of existing antibiotics in order to improve medical outcomes, decrease toxicity and reduce the emergence of resistance. We formulate the design of antibiotic dosing regimens as a continuous optimisation problem and use several evolutionary algorithms as the search technique. Regimens are represented as vectors of real numbers encoding daily doses, which can vary across the treatment duration. A stochastic mathematical model of bacterial infections with tuneable resistance levels is used to evaluate the effectiveness of evolved regimens. The main objective is to minimise the treatment failure rate, subject to a constraint on the maximum total antibiotic used. We consider simulations with different levels of bacterial resistance; two ways of administering the drug (orally and intravenously); as well as coinfections with two strains of bacteria. The approach produced effective dosing regimens, with an average improvement in lowering the failure rate 30%, when compared with standard fixed-daily-dose regimens with the same total amount of antibiotic. A general pattern of an optimised treatment is found, where if 2x is the standard daily dose then the optimised treatment follows the 3x mg, followed by several 2x mg with a last dose of x mg. A noise handling technique is used to minimise the runtime of the experiments while maintaining the quality of treatments. The results of this work indicate that clinical studies confirming the effectiveness of this approach could be highly beneficial to future of antibiotic treatments.

Antibiotic resistance is one of the major health concerns of the 21st century. Antibiotics are essential for the health and well-being of both humans and animals. However, the increase in antibiotic resistant bacteria poses a threat to the continued use of antibiotics to successfully treat bacterial infections. Current research within hospital settings has focused on the use of multi-antibiotic approaches in a variety of treatment patterns. Yet there is limited knowledge on the optimal use of single antibiotic treatments. With the spread of resistance linked to the overuse and misuse of antibiotics, optimal treatment regimens aim to maximise the success of eradicating an infection while minimising the amount of antibiotic required. This thesis therefore aimed to combine mathematical modelling with a genetic algorithm approach to identify optimal dosage regimens for the use of a single antibiotic. A mathematical model was developed to predict the dynamics of bacterial populations within an infection. A susceptible only infection was initially considered before being extended to include a resistant population. These models were incorporated into a genetic algorithm and used to search for dosage regimens which maximise bacterial eradication and minimise antibiotic use. Taking a theoretical approach, it was found that administering an antibiotic with a high initial dose followed by lowering doses is the optimal treatment regimen. A case study of a Vibrio anguillarum infection within Galleria mellonella larvae was used to parameterise the one strain bacterial model to a biologically realistic system. The results are consistent with those from the theoretical parameter sets. A tapered treatment regimen maximises the success of eradicating the bacterial infection while minimising the amount of antibiotic required. Laboratory experiments were performed which provided credibility to the results found. Finally, the assumption of fixed time intervals between doses was relaxed and the genetic algorithm used to identify both the dose and time intervals of optimal treatment regimens. Varying either the doses or the time intervals separately produced no significant difference in the success of eradicating an infection. When combined, the results showed that significantly better regimens could be identified. These regimens further increased bacterial eradication while using less antibiotic to do so. More work is required to identify a general treatment pattern when both variables are optimised due to the high variability in solutions. However, a shift away from conventional constant dose treatment regimens is required to prolong the future effectiveness of antibiotics.

Multi-scale modelling and analysis is becoming increasingly important and relevant. Analysis of the emergent properties from the interactions between scales of multi-scale systems is important to aid in solutions. There is no universally adopted theoretical/computational framework or language for the construction of multi-scale models. Most modelling approaches are specific to the problem that they are addressing and use a hybrid combination of modelling languages to model specific scales. This thesis addresses if process algebra can offer a unique opportunity in the definition and analysis of multi-scale models. In this thesis the generic Process Algebra with Layers (PAL) is defined: a language for multi-scale integration modelling. This work highlights the potential of process algebra to model multi-scale systems. PAL was designed based on features and challenges found from modelling a multi-scale system in an existing process algebra. The unique features of PAL are the layers: Population and Organism. The novel language modularises the spatial scales of the system into layers, therefore, modularising the detail of each scale. An Organism can represent a molecule, organelle, cell, tissue, organ or any organism. An Organism is described by internal species. An internal species, dependent on the scale of the Organism, can also represent a molecule, organelle, cell, tissue, organ or any organism. Populations hold specific types of Organism, for example, life stages, cell phases, infectious states and many more. The Population and Organism layers are integrated through mirrored actions. This novel language allows the clear definition of scales and interactions within and between these scales in one model. PAL can be applied to define a variety of multi-scale systems. PAL has been applied to two unrelated multi-scale system case studies to highlight the advantages of the generic novel language. Firstly the effects of ocean acidification on the life stages of the Pacific oyster. Secondly the effects of DNA damage from cancer treatment on the length of a cell cycle and cell population growth.

Natural populations may be managed by humans for a number of reasons, with mathematical modelling playing an increasing role in the planning of such management and control strategies. In an increasingly heterogeneous, or `patchy' landscape, the interactions between distinct groups of individuals must be taken into account to predict meaningful management strategies. Invasive control strategies, involving reduction of populations, such as harvesting or culling have been shown to cause a level of disturbance, or spatial perturbation, to these groups, a factor which is largely ignored in the modelling literature. In this thesis, we present a series of deterministic, differential equation models which are used to investigate the impact of this disturbance in response to control. We address this impact in two scenarios. Firstly, in terms of a harvested population, where extinction must be prevented whilst maximising the yield obtained. Secondly, we address the impact of disturbance in an epidemic model, where the aim of the control strategy is to eradicate an endemic pathogen, or to prevent the invasion of a pathogen into a susceptible population. The movement of individuals between patches is modelled as both a constant rate, and a function which is increasing with population density. Finally, we discuss the 'optimal' control strategy in this context. We find that, whilst a population harvested from a coupled system is able to produce an inflated yield, this coupling can also cause the population to be more resistant to higher harvesting efforts, increasing the effort required to drive the population to extinction. Spatial perturbation raises this extinction threshold further still, providing a survival mechanism not only for the individuals that avoid being killed, but for the population as a whole. With regards to the eradication of disease, we show that disturbance may either raise or lower the pathogen exclusion threshold depending on the particular characteristics of the pathogen. In certain cases, we have shown that spatial perturbation may force a population to be susceptible to an infectious invasion where its natural carrying capacity would prevent this.

Species of Argulus are macro-, ecto-parasites known to infect a wide variety of fish, but in the UK mainly cause problems in rainbow (Oncorhynchus mykiss) and brown trout (Salmo trutta). Argulus foliaceus is estimated to have caused problems in over 25% of stillwater trout fisheries in the UK. While A. foliaceus does not usually cause high levels of mortality, the parasite affects fish welfare, and also makes fish harder to catch due to morbidity and reduced appetite. This can cause severe economic problems for the fishery, resulting in reduced angler attendance due to poor capture rates and the reduced aesthetic appearance of fish; in the worst-case scenario this can result in the closure of the fishery. Current methods of control include chemical treatment with chemotherapeutant emamectin benzoate (Slice), physical intervention with egg-laying boards which are removed periodically and cleaned in order to reduce the number of parasites hatching into the environment, and the complete draining and liming of the lake to remove all free-living and egg stages of the parasite. While these treatments have all been shown to reduce parasite numbers, none are known to have resulted in permament eradication of the parasite. There is evidence to suggest that A. foliaceus will eventually develop resistance to Slice - the only currently available chemical treatment against the infection - and egg-laying boards and the draining and liming of the lake are both time- and labour-intensive. Previous studies have shown that slow fish turnover is a risk factor with respect to A. foliaceus infections, and with a wide variety of stocking practices occurring in the UK one of the first aims of this project was to determine their impact on the host-parasite dynamics. Mathematical models provide a cost-effective way of examining the impact of such practices, and after a literature review (chapter one), in chapter two a three-compartment mathematical model was adapted for use in the A. foliaceus-trout system. Four generalised stocking methods were then incorporated and analysed, and a minimum threshold host density was found to be necessary to sustain the parasite. Including a function which reduced the capture rate as the parasite burden increased allowed the parasite to survive at a lower host density, as susceptible fish were removed from the water at a slower rate, and attached parasites also remained in the water for longer. This resulted in hysteresis in the model, as the invasion threshold for the parasite remained the same, but once established the parasite became harder to eradicate, requiring significant reductions in the host density. In chapter three the model was further developed in order to improve its biological real- ism. Several features were added and these included: natural host mortalities, a separate compartment for the parasite egg population, and parasite survival after the natural or parasite-induced mortality of its host. In chapter four seasonality was added by incorporating temperature-dependent egg-laying rates and an over-wintering period during which the parasite was unable to reproduce. The model was then fit to the available data, and estimates for the rate of parasite-induced host mortalities and the parasite’s rate of attachment to a host were found. In chapter five we returned to stocking methods, this time looking at the frequency and timing of stocking events and the impact of imposing a rod limit (whereby anglers are only permitted to capture four fish per visit); it was concluded that while current guidelines suggest that very frequent trickle stocking is recommended when dealing with Argulus spp. infections, monthly stocking does not appear to worsen the infection, and if the fish capture rate is high then less-frequent stocking may also be permissable - particularly if stocking occurs towards the end of the year when the parasite is no longer active. This practice may, however, be detrimental to the fishery due to low fish densities in the summer months. In chapter six treatment with Slice was included in the model, and it was demonstrated that with constant treatment, and in the absence of reservoir hosts and a withdrawal period from the drug prior to stocking treated fish into the fishery, the parasite was eradicated. Under current veterinary cascade guidelines, however, trout are required to undergo a withdrawal period of 500 degree days prior to being made available for human consumption. When this was included in the model the drug still decreased parasite abundance, but did not eradicate it - this is in agreement with results reported by communications with fishery managers currently treating fish with Slice. A reduction in the withdrawal period of 25% was shown to further decrease parasite abundance, but still did not result in parasite extinction. As constant treatment with Slice is not advisable due to the potential for resistance build-up, we then sought to find time at which to apply a single treatment of Slice, and found that this was in August when the temperature was highest and the parasite was reproducing and attaching to hosts quickly. Egg-laying boards were also incorporated into the model and similarly to findings by Fenton et al. [11] the success of this treatment was mostly dependent on the proportion of eggs being laid on the boards (as opposed to natural substrates). In contrast with the A. coregoni system, however, the boards would have to be cleaned and replaced more frequently that once per year, as several cohorts of A. foliaceus emerge during a single year.

Gyrodactylus salaris Malmberg, 1957, is a notifiable freshwater ecto-parasite that infects both wild and farmed populations of Atlantic salmon (Salmo salar, L.). It has caused catastrophic damage to wild salmon stocks in Norway since its accidental introduction in 1975, reducing salmon density in some rivers by 98% over a period of five years. It is estimated that G. salaris has cost the Norwegian salmon industry more than 500 million EUR. Currently the UK has G. salaris free status under EU law, however, it is believed that if G. salaris emerged in the UK the impact would be similar to that witnessed in Norway. The aim of this thesis is to develop mathematical models that describe the salmon-G. salaris system in order to gain a greater understanding of the possible long-term impact the parasite may have on wild populations of Atlantic salmon in G. salaris-free territories such as the UK. Mathematical models, including deterministic, Leslie matrix and individual based models, were used to investigate the impact of G. salaris on Atlantic salmon at the individual and population level. It is known that the Atlantic strain of Atlantic salmon, examples of which occur naturally in Norway and the UK, does not have any resistance to G. salaris infections and the parasite population is able to quickly grow to epidemic levels. In contrast, the Baltic strain of Atlantic salmon, examples of which occur naturally in Sweden and Russia, exhibits some form of resistance and the parasite is unable to persist. Thus, baseline models were extended to include immunity to infection, a trade-off on salmon reproductive rate, and finally, to consider interactions between populations of G. salaris and multiple strains of salmon exhibiting varying levels of immunity from fully susceptible to resistant. The models proposed predict that in the absence of host resistance or an immune response infections by G. salaris will result in an epidemic followed by the extinction of the salmon host population. Models also predict that if salmon are able to increase their resistance to G. salaris infections through mutations, salmon population recovery after the epidemic is indeed possible within 10-15 years post introduction with low level parasite coexistence. Finally, models also highlight areas where additional information is needed in order to improve predictions and enable the estimation of important parameter values. Model predictions will ultimately be used to assist in future contingency planning against G. salaris outbreaks in the UK and possibly as a basis for future models describing other fish/ecto-parasite systems.