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Malaria remains a global health problem despite the many attempts to control and eradicate it. There is an urgent need to understand the current transmission dynamics of malaria and to determine the interventions necessary to control malaria. In this paper, we seek to develop a fit-for-purpose mathematical model to assess the interventions needed to control malaria in an endemic setting. To achieve this, we formulate a malaria transmission model to analyse the spread of malaria in the presence of interventions. A sensitivity analysis of the model is performed to determine the relative impact of the model parameters on disease transmission. We explore how existing variations in the recruitment and management of intervention strategies affect malaria transmission. Results obtained from the study imply that the discontinuation of existing interventions has a significant effect on malaria prevalence. Thus, the maintenance of interventions is imperative for malaria elimination and eradication. In a scenario study aimed at assessing the impact of long-lasting insecticidal nets (LLINs), indoor residual spraying (IRS), and localized individual measures, our findings indicate that increased LLINs utilization and extended IRS coverage (with longer-lasting insecticides) cause a more pronounced reduction in symptomatic malaria prevalence compared to a reduced LLINs utilization and shorter IRS coverage. Additionally, our study demonstrates the impact of localized preventive measures in mitigating the spread of malaria when compared to the absence of interventions. [ABSTRACT FROM AUTHOR]

Many threats to biodiversity cannot be eliminated; for example, invasive pathogens may be ubiquitous. Chytridiomycosis is a fungal disease that has spread worldwide, driving at least 90 amphibian species to extinction, and severely affecting hundreds of others1–4. Once the disease spreads to a new environment, it is likely to become a permanent part of that ecosystem. To enable coexistence with chytridiomycosis in the field, we devised an intervention that exploits host defences and pathogen vulnerabilities. Here we show that sunlight-heated artificial refugia attract endangered frogs and enable body temperatures high enough to clear infections, and that having recovered in this way, frogs are subsequently resistant to chytridiomycosis even under cool conditions that are optimal for fungal growth. Our results provide a simple, inexpensive and widely applicable strategy to buffer frogs against chytridiomycosis in nature. The refugia are immediately useful for the endangered species we tested and will have broader utility for amphibian species with similar ecologies. Furthermore, our concept could be applied to other wildlife diseases in which differences in host and pathogen physiologies can be exploited. The refugia are made from cheap and readily available materials and therefore could be rapidly adopted by wildlife managers and the public. In summary, habitat protection alone cannot protect species that are affected by invasive diseases, but simple manipulations to microhabitat structure could spell the difference between the extinction and the persistence of endangered amphibians.Artificial thermal refugia—sites heated to temperatures higher than that of the surrounding environment—provide a way to protect an endangered Australian frog species from a fungal disease that has caused the extinction of many amphibians. [ABSTRACT FROM AUTHOR]

Malaria is a vector-borne disease that exacts a grave toll in the Global South. The epidemiology of Plasmodium vivax, the most geographically expansive agent of human malaria, is characterised by the accrual of a reservoir of dormant parasites known as hypnozoites. Relapses, arising from hypnozoite activation events, comprise the majority of the blood-stage infection burden, with implications for the acquisition of immunity and the distribution of superinfection. Here, we construct a novel model for the transmission of P. vivax that concurrently accounts for the accrual of the hypnozoite reservoir, (blood-stage) superinfection and the acquisition of immunity. We begin by using an infinite-server queueing network model to characterise the within-host dynamics as a function of mosquito-to-human transmission intensity, extending our previous model to capture a discretised immunity level. To model transmission-blocking and antidisease immunity, we allow for geometric decay in the respective probabilities of successful human-to-mosquito transmission and symptomatic blood-stage infection as a function of this immunity level. Under a hybrid approximation—whereby probabilistic within-host distributions are cast as expected population-level proportions—we couple host and vector dynamics to recover a deterministic compartmental model in line with Ross-Macdonald theory. We then perform a steady-state analysis for this compartmental model, informed by the (analytic) distributions derived at the within-host level. To characterise transient dynamics, we derive a reduced system of integrodifferential equations, likewise informed by our within-host queueing network, allowing us to recover population-level distributions for various quantities of epidemiological interest. In capturing the interplay between hypnozoite accrual, superinfection and acquired immunity—and providing, to the best of our knowledge, the most complete population-level distributions for a range of epidemiological values—our model provides insights into important, but poorly understood, epidemiological features of P. vivax. [ABSTRACT FROM AUTHOR]

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages. [ABSTRACT FROM AUTHOR]

Plasmodium vivax is the most geographically widespread malaria-causing parasite resulting in significant associated global morbidity and mortality. One of the factors driving this widespread phenomenon is the ability of the parasites to remain dormant in the liver. Known as 'hypnozoites', they reside in the liver following an initial exposure, before activating later to cause further infections, referred to as 'relapses'. As around 79–96% of infections are attributed to relapses from activating hypnozoites, we expect it will be highly impactful to apply treatment to target the hypnozoite reservoir (i.e. the collection of dormant parasites) to eliminate P. vivax. Treatment with radical cure, for example tafenoquine or primaquine, to target the hypnozoite reservoir is a potential tool to control and/or eliminate P. vivax. We have developed a deterministic multiscale mathematical model as a system of integro-differential equations that captures the complex dynamics of P. vivax hypnozoites and the effect of hypnozoite relapse on disease transmission. Here, we use our multiscale model to study the anticipated effect of radical cure treatment administered via a mass drug administration (MDA) program. We implement multiple rounds of MDA with a fixed interval between rounds, starting from different steady-state disease prevalences. We then construct an optimisation model with three different objective functions motivated on a public health basis to obtain the optimal MDA interval. We also incorporate mosquito seasonality in our model to study its effect on the optimal treatment regime. We find that the effect of MDA interventions is temporary and depends on the pre-intervention disease prevalence (and choice of model parameters) as well as the number of MDA rounds under consideration. The optimal interval between MDA rounds also depends on the objective (combinations of expected intervention outcomes). We find radical cure alone may not be enough to lead to P. vivax elimination under our mathematical model (and choice of model parameters) since the prevalence of infection eventually returns to pre-MDA levels. [ABSTRACT FROM AUTHOR]

In vitro experiments in which tumour cells are seeded in a gelatinous medium, or hydrogel, show how mechanical interactions between tumour cells and the tissue in which they are embedded, together with local levels of an externally-supplied, diffusible nutrient (e.g., oxygen), affect the tumour’s growth dynamics. In this article, we present a mathematical model that describes these in vitro experiments. We use the model to understand how tumour growth generates mechanical deformations in the hydrogel and how these deformations in turn influence the tumour’s growth. The hydrogel is viewed as a nonlinear hyperelastic material and the tumour is modelled as a two-phase mixture, comprising a viscous tumour cell phase and an isotropic, inviscid interstitial fluid phase. Using a combination of numerical and analytical techniques, we show how the tumour’s growth dynamics change as the mechanical properties of the hydrogel vary. When the hydrogel is soft, nutrient availability dominates the dynamics: the tumour evolves to a large equilibrium configuration where the proliferation rate of nutrient-rich cells on the tumour boundary balances the death rate of nutrient-starved cells in the central, necrotic core. As the hydrogel stiffness increases, mechanical resistance to growth increases and the tumour’s equilibrium size decreases. Indeed, for small tumours embedded in stiff hydrogels, the inhibitory force experienced by the tumour cells may be so large that the tumour is eliminated. Analysis of the model identifies parameter regimes in which the presence of the hydrogel drives tumour elimination. [ABSTRACT FROM AUTHOR]

Malaria is caused by Plasmodium parasites which are transmitted to humans by the bite of an infected Anopheles mosquito. Plasmodium vivax is distinct from other malaria species in its ability to remain dormant in the liver (as hypnozoites) and activate later to cause further infections (referred to as relapses). Mathematical models to describe the transmission dynamics of P. vivax have been developed, but most of them fail to capture realistic dynamics of hypnozoites. Models that do capture the complexity tend to involve many governing equations, making them difficult to extend to incorporate other important factors for P. vivax, such as treatment status, age and pregnancy. In this paper, we have developed a multiscale model (a system of integro-differential equations) that involves a minimal set of equations at the population scale, with an embedded within-host model that can capture the dynamics of the hypnozoite reservoir. In this way, we can gain key insights into dynamics of P. vivax transmission with a minimum number of equations at the population scale, making this framework readily scalable to incorporate more complexity. We performed a sensitivity analysis of our multiscale model over key parameters and found that prevalence of P. vivax blood-stage infection increases with both bite rate and number of mosquitoes but decreases with hypnozoite death rate. Since our mathematical model captures the complex dynamics of P. vivax and the hypnozoite reservoir, it has the potential to become a key tool to inform elimination strategies for P. vivax. [ABSTRACT FROM AUTHOR]

In many countries, concerns have been raised regarding the lack of participation of students in mathematics at the university level due to a dearth of skilled professionals to meet the needs of an increasingly technological, and thus mathematical, world. In this article, we report findings from a study in which we compared the experiences of first-year and final-year undergraduate students studying in the mathematics departments at two Australian universities. We focus on the participants' conceptions of the supports and challenges that they experienced in the mathematics departments, using a multimodal data collection method, photovoice. We found key differences between first-year and final-year participants' perceptions of the learning environment when considering gender-related differences, such as an increasingly lower participation of women in mathematics and differential treatment by gender. Participants reported feeling supported by peers, at both year levels, and faculty members, particularly in first year. Participants from both year levels valued the collaborative learning environment of the classes and technological learning supports (e.g. lecture recordings) but raised concerns about the format and weighting of assessments. Although there were some year level differences, there were also commonalities to the participants' experiences, which indicates that some issues may be systemic. The knowledge that is gained from this research is crucial in understanding students' lived experiences and thus making suggestions to address university mathematics pipeline issues. [ABSTRACT FROM AUTHOR]

Malaria is a mosquito-borne disease that, despite intensive control and mitigation initiatives, continues to pose an enormous public health burden. Plasmodium vivax is one of the principal causes of malaria in humans. Antibodies, which play a fundamental role in the host response to P. vivax, are acquired through exposure to the parasite. Here, we introduce a stochastic, within-host model of antibody responses to P. vivax for an individual in a general transmission setting. We begin by developing an epidemiological framework accounting for P. vivax infections resulting from new mosquito bites (primary infections), as well as the activation of dormant-liver stages known as hypnozoites (relapses). By constructing an infinite server queue, we obtain analytic results for the distribution of relapses in a general transmission setting. We then consider a simple model of antibody kinetics, whereby antibodies are boosted with each infection, but are subject to decay over time. By embedding this model for antibody kinetics in the epidemiological framework using a generalised shot noise process, we derive analytic expressions governing the distribution of antibody levels for a single individual in a general transmission setting. Our work provides a means to explore exposure-dependent antibody dynamics for P. vivax, with the potential to address key questions in the context of serological surveillance and acquired immunity. [ABSTRACT FROM AUTHOR]

In this paper we present a novel method for finding unknown parameters for an unknown morphogen. We postulate the existence of an unknown morphogen in a given three-dimensional domain due to the spontaneous arrangement of a downstream species on the domain boundary for which data is known. Assuming a modified Helmholtz model for the morphogen and that it is produced from a single source in the domain, our method accurately estimates the source location and other model parameters. Notably, our method does not require the forward solution of the model to be computed which can often be a challenge for three-dimensional PDE model parameter fitting. Instead, an extension is made from the problem domain to an infinite domain and the analytic nature of the fundamental solution is exploited. We explore in this manuscript strategies for best conditioning the problem and rigorously explore the accuracy of the method on two test problems. Our tests focus on the effect of source location on accuracy but also the robustness of the algorithm to experimental noise. [ABSTRACT FROM AUTHOR]

Angiogenesis, or capillary growth from pre-existing vasculature, is an essential component of several physiological processes, both vital and pathological. These include dermal wound healing and tumour growth that together pose some of the most significant challenges to healthcare systems worldwide. Over the last few decades, mathematical modelling has proven to be a valuable tool for unravelling the complex network of interactions that underlie such processes. Moreover, theoretical frameworks that describe some of the mechanical and chemical aspects of angiogenesis inherent in wound healing and tumour growth have revealed intriguing similarities between the two processes. In this review, we highlight some of the significant contributions made by mathematical models of tumour-induced and wound healing angiogenesis and illustrate how advances in each field have been made using insights from the other. We also detail some open problems that could be addressed through a combination of theoretical and experimental approaches. [ABSTRACT FROM AUTHOR]

Malaria is an infectious disease with an immense global health burden. Plasmodium vivax is the most geographically widespread species of malaria. Relapsing infections, caused by the activation of liver-stage parasites known as hypnozoites, are a critical feature of the epidemiology of Plasmodium vivax. Hypnozoites remain dormant in the liver for weeks or months after inoculation, but cause relapsing infections upon activation. Here, we introduce a dynamic probability model of the activation-clearance process governing both potential relapses and the size of the hypnozoite reservoir. We begin by modelling activation-clearance dynamics for a single hypnozoite using a continuous-time Markov chain. We then extend our analysis to consider activation-clearance dynamics for a single mosquito bite, which can simultaneously establish multiple hypnozoites, under the assumption of independent hypnozoite behaviour. We derive analytic expressions for the time to first relapse and the time to hypnozoite clearance for mosquito bites establishing variable numbers of hypnozoites, both of which are quantities of epidemiological significance. Our results extend those in the literature, which were limited due to an assumption of collective dormancy. Our within-host model can be embedded readily in multiscale models and epidemiological frameworks, with analytic solutions increasing the tractability of statistical inference and analysis. Our work therefore provides a foundation for further work on immune development and epidemiological-scale analysis, both of which are important for achieving the goal of malaria elimination. [ABSTRACT FROM AUTHOR]

Cancer is a global health burden; 1 in 2 people will be diagnosed with some form of cancer during their lifetime. In the Western world, 50% of cancer patients survive for 10 or more years after diagnosis, compared to 24% forty years earlier. Cancer can come in many different forms, but tissues affected by cancer tend to have common features such as abnormal cell growth rates. Cancer biology is incredibly complicated, as illustrated by the difficulties surrounding the diagnosis and treatment of cancer. However, mathematics has the potential to mediate this complexity by abstracting the system using simplifying assumptions into a mathematical framework that can be analysed and/or solved numerically to gain biological insight. This article is an introduction to the mathematical modelling of one of the important early stages of tumour growth — the avascular stage — where there is no blood supply to the tumour. [ABSTRACT FROM AUTHOR]

The failure of certain wounds to heal (including diabetic foot ulcers) is a significant socioeconomic issue for countries worldwide. There is much debate about the best way to treat these wounds and one approach that is shrouded with controversy is hyperbaric oxygen therapy (HBOT), a technique that can reduce the risk of amputation in diabetic patients. In this paper, we develop a six species mathematical model of wound healing angiogenesis and use it to investigate the effectiveness of HBOT, compare the response to different HBOT protocols and study the effect of HBOT on the healing of diabetic wounds that fail to heal for a variety of reasons. We vary the pressure level (1 atm-3 atm), percentage of oxygen inspired by the patient (21%-100%), session duration (0-180 minutes) and frequency (twice per day-once per week) and compare the simulated wound areas associated with different protocols after three weeks of treatment. We consider a variety of etiologies of wound chronicity and show that HBOT is only effective in treating certain causes of chronic wounds. For a wound that fails to heal due to excessive, oxygen-consuming bacteria, we show that intermittent HBOT can accelerate the healing of a chronic wound but that sessions should be continued until complete healing is observed. Importantly, we also demonstrate that normobaric oxygen is not a replacement for HBOT and supernormal healing is not an expected outcome. Our simulations illustrate that HBOT has little benefit for treating normal wounds, and that exposing a patient to fewer, longer sessions of oxygen is not an appropriate treatment option. [ABSTRACT FROM AUTHOR]

We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A limiting nutrient that follows a diffusion process controls the birth and death rate of the tumour cells. The cell volume fraction, cell velocity–fluid pressure system, and nutrient concentration are the model variables. A coupled system of a hyperbolic conservation law, a viscous fluid model, and a parabolic diffusion equation governs the dynamics of the model variables. The tumour boundary moves with the normal velocity of the outermost layer of cells, and this time-dependence is a challenge in designing and implementing a stable and fast numerical scheme. We recast the model into a form where the hyperbolic equation is defined on a fixed extended domain and retrieve the tumour boundary as the interface at which the cell volume fraction decreases below a threshold value. This procedure eliminates the need to track the tumour boundary explicitly and the computationally expensive re-meshing of the time-dependent domains. A numerical scheme based on finite volume methods for the hyperbolic conservation law, Lagrange P 2 - P 1 Taylor-Hood finite element method for the viscous system, and mass-lumped finite element method for the parabolic equations is implemented in two spatial dimensions, and several cases are studied. We demonstrate the versatility of the numerical scheme in catering for irregular and asymmetric initial tumour geometries. When the nutrient diffusion equation is defined only in the tumour region, the model depicts growth in free suspension. On the contrary, when the nutrient diffusion equation is defined in a larger fixed domain, the model depicts tumour growth in a polymeric gel. We present numerical simulations for both cases and the results are consistent with theoretical and heuristic expectations such as early linear growth rate and preservation of radial symmetry when the boundary conditions are symmetric. The work presented here could be extended to include the effect of drug treatment of growing tumours. [ABSTRACT FROM AUTHOR]