Agent-Based and Continuum Models for Spatial Dynamics of Infection by Oncolytic Viruses.

The use of oncolytic viruses as cancer treatment has received considerable attention in recent years, however the spatial dynamics of this viral infection is still poorly understood. We present here a stochastic agent-based model describing infected and uninfected cells for solid tumours, which interact with viruses in the absence of an immune response. Two kinds of movement, namely undirected random and pressure-driven movements, are considered: the continuum limit of the models is derived and a systematic comparison between the systems of partial differential equations and the individual-based model, in one and two dimensions, is carried out. In the case of undirected movement, a good agreement between agent-based simulations and the numerical and well-known analytical results for the continuum model is possible. For pressure-driven motion, instead, we observe a wide parameter range in which the infection of the agents remains confined to the center of the tumour, even though the continuum model shows traveling waves of infection; outcomes appear to be more sensitive to stochasticity and uninfected regions appear harder to invade, giving rise to irregular, unpredictable growth patterns. Our results show that the presence of spatial constraints in tumours' microenvironments limiting free expansion has a very significant impact on virotherapy. Outcomes for these tumours suggest a notable increase in variability. All these aspects can have important effects when designing individually tailored therapies where virotherapy is included.

Modelling accessibility of adult neurology care in Australia, 2020-2034.

Introduction: In 2015/2016, annual national expenditure on neurological conditions exceeded $A3 billion. However, a comprehensive study of the Australian neurological workforce and supply/demand dynamics has not previously been undertaken. Methods: Current neurological workforce was defined using neurologist survey and other sources. Workforce supply modelling used ordinary differential equations to simulate neurologist influx and attrition. Demand for neurology care was estimated by reference to literature regarding incidence and prevalence of selected conditions. Differences in supply versus demand for neurological workforce were calculated. Potential interventions to increase workforce were simulated and effects on supply versus demand estimated. Results: Modelling of the workforce from 2020 to 2034 predicted an increase in neurologist number from 620 to 89. We estimated a 2034 capacity of 638 024 Initial and 1 269 112 Review encounters annually, and deficits against demand estimated as 197 137 and 881 755, respectively. These deficits were proportionately greater in regional Australia, which has 31% of Australia's population (Australian Bureau of Statistics) but is served by only 4.1% of its neurologists as determined by our 2020 survey of Australia and New Zealand Association of Neurologists members. Nationally, simulated additions to the neurology workforce had some effect on the review encounter supply deficit (37.4%), but in Regional Australia, this impact was only 17.2%. Interpretation: Modelling of the neurologist workforce in Australia for 2020-2034 demonstrates a significant shortfall of supply relative to current and projected demand. Interventions to increase neurologist workforce may attenuate this shortfall but will not eliminate it. Thus, additional interventions are needed, including improved efficiency and additional use of support staff.

The dynamics of relapses during treatment switch in relapsing-remitting multiple sclerosis.

Based on reported trends in relapse incidence among patients with relapsing-remitting multiple sclerosis, an original model for the response to disease modifying therapies is proposed. With a population approach and separate states for patients accounting for their risk of relapses, a system of nonlinear equations is formulated, similarly to established epidemiological models. Different parameters describe the effect of drugs and treatment switch in reducing the frequency of relapses. The model allows for a good fit to previously published data for experiments where different drugs are used. It also shows that different treatments maintain a high degree of similarity, with analogous dynamical features: a pre-treatment increment in relapse frequency leading to a distinct peak, a rapid drop after treatment switch and a plateau corresponding to a new base relapse activity, which seems dependant on the treatment chosen. A sensitivity analysis shows that the uncertainty in the initial proportions of different populations and the frequency of relapses can modify the overall dynamics of the response to treatment. Drugs are observed to induce effects that depend on patient sample's intrinsic characteristics, producing two clearly distinct and independent dynamics of relapse response. This confirms the clinical observation that certain drugs may be overall more successful in lowering the rate of relapses more significantly than others, notwithstanding the fact that patients behave differently across experiments.

An investigation of tuberculosis progression revealing the role of macrophages apoptosis via sensitivity and bifurcation analysis.

Mycobacterium tuberculosis infection features various disease outcomes: clearance, latency, active disease, and latent tuberculosis infection (LTBI) reactivation. Identifying the decisive factors for disease outcomes and progression is crucial to elucidate the macrophages-tuberculosis interaction and provide insights into therapeutic strategies. To achieve this goal, we first model the disease progression as a dynamical shift among different disease outcomes, which are characterized by various steady states of bacterial concentration. The causal mechanisms of steady-state transitions can be the occurrence of transcritical and saddle-node bifurcations, which are induced by slowly changing parameters. Transcritical bifurcation, occurring when the basic reproduction number equals to one, determines whether the infection clears or spreads. Saddle-node bifurcation is the key mechanism to create and destroy steady states. Based on these two steady-state transition mechanisms, we carry out two sample-based sensitivity analyses on transcritical bifurcation conditions and saddle-node bifurcation conditions. The sensitivity analysis results suggest that the macrophage apoptosis rate is the most significant factor affecting the transition in disease outcomes. This result agrees with the discovery that the programmed cell death (apoptosis) plays a unique role in the complex microorganism-host interplay. Sensitivity analysis narrows down the parameters of interest, but cannot answer how these parameters influence the model outcomes. To do this, we employ bifurcation analysis and numerical simulation to unfold various disease outcomes induced by the variation of macrophage apoptosis rate. Our findings support the hypothesis that the regulation mechanism of macrophage apoptosis affects the host immunity against tuberculosis infection and tuberculosis virulence. Moreover, our mathematical results suggest that new treatments and/or vaccines that regulate macrophage apoptosis in combination with weakening bacillary viability and/or promoting adaptive immunity could have therapeutic value.

The phase space distribution of confined fluids under shear is not fractal.

We analyze the phase-space compression, characteristic of all deterministic, dissipative systems for an inhomogeneous boundary-driven shear fluid via nonequilibrium molecular dynamics simulations. We find that, although the full system undergoes a phase space contraction, the marginal distribution of the fluid particles is described by a smooth, volume preserving probability density function. This is the case for most thermodynamic states of physical interest. Hence, we show that the models currently employed to investigate inhomogeneous fluids in a nonequilibrium steady state, in which only walls are thermostatted, generate a non-singular distribution for the fluid.

Determinants of therapeutic lag in multiple sclerosis.

BACKGROUND: A delayed onset of treatment effect, termed therapeutic lag, may influence the assessment of treatment response in some patient subgroups. OBJECTIVES: The objective of this study is to explore the associations of patient and disease characteristics with therapeutic lag on relapses and disability accumulation. METHODS: Data from MSBase, a multinational multiple sclerosis (MS) registry, and OFSEP, the French MS registry, were used. Patients diagnosed with MS, minimum 1 year of exposure to MS treatment and 3 years of pre-treatment follow-up, were included in the analysis. Studied outcomes were incidence of relapses and disability accumulation. Therapeutic lag was calculated using an objective, validated method in subgroups stratified by patient and disease characteristics. Therapeutic lag under specific circumstances was then estimated in subgroups defined by combinations of clinical and demographic determinants. RESULTS: High baseline disability scores, annualised relapse rate (ARR) ⩾ 1 and male sex were associated with longer therapeutic lag on disability progression in sufficiently populated groups: females with expanded disability status scale (EDSS) < 6 and ARR < 1 had mean lag of 26.6 weeks (95% CI = 18.2-34.9), males with EDSS < 6 and ARR < 1 31.0 weeks (95% CI = 25.3-36.8), females with EDSS < 6 and ARR ⩾ 1 44.8 weeks (95% CI = 24.5-65.1), and females with EDSS ⩾ 6 and ARR < 1 54.3 weeks (95% CI = 47.2-61.5). CONCLUSIONS: Pre-treatment EDSS and ARR are the most important determinants of therapeutic lag.

The role of viral infectivity in oncolytic virotherapy outcomes: A mathematical study.

A model capturing the dynamics between virus and tumour cells in the context of oncolytic virotherapy is presented and analysed. The ability of the virus to be internalised by uninfected cells is described by an infectivity parameter, which is inferred from available experimental data. The parameter is also able to describe the effects of changes in the tumour environment that affect viral uptake from tumour cells. Results show that when a virus is inoculated inside a growing tumour, strategies for enhancing infectivity do not lead to a complete eradication of the tumour. Within typical times of experiments and treatments, we observe the onset of oscillations, which always prevent a full destruction of the tumour mass. These findings are in good agreement with available laboratory results. Further analysis shows why a fully successful therapy cannot exist for the proposed model and that care must be taken when designing and engineering viral vectors with enhanced features. In particular, bifurcation analysis reveals that creating longer lasting virus particles or using strategies for reducing infected cell lifespan can cause unexpected and unwanted surges in the overall tumour load over time. Our findings suggest that virotherapy alone seems unlikely to be effective in clinical settings unless adjuvant strategies are included.

Delay from treatment start to full effect of immunotherapies for multiple sclerosis.

In multiple sclerosis, treatment start or switch is prompted by evidence of disease activity. Whilst immunomodulatory therapies reduce disease activity, the time required to attain maximal effect is unclear. In this study we aimed to develop a method that allows identification of the time to manifest fully and clinically the effect of multiple sclerosis treatments ('therapeutic lag') on clinical disease activity represented by relapses and progression-of-disability events. Data from two multiple sclerosis registries, MSBase (multinational) and OFSEP (French), were used. Patients diagnosed with multiple sclerosis, minimum 1-year exposure to treatment, minimum 3-year pretreatment follow-up and yearly review were included in the analysis. For analysis of disability progression, all events in the subsequent 5-year period were included. Density curves, representing incidence of relapses and 6-month confirmed progression events, were separately constructed for each sufficiently represented therapy. Monte Carlo simulations were performed to identify the first local minimum of the first derivative after treatment start; this point represented the point of stabilization of treatment effect, after the maximum treatment effect was observed. The method was developed in a discovery cohort (MSBase), and externally validated in a separate, non-overlapping cohort (OFSEP). A merged MSBase-OFSEP cohort was used for all subsequent analyses. Annualized relapse rates were compared in the time before treatment start and after the stabilization of treatment effect following commencement of each therapy. We identified 11 180 eligible treatment epochs for analysis of relapses and 4088 treatment epochs for disability progression. External validation was performed in four therapies, with no significant difference in the bootstrapped mean differences in therapeutic lag duration between registries. The duration of therapeutic lag for relapses was calculated for 10 therapies and ranged between 12 and 30 weeks. The duration of therapeutic lag for disability progression was calculated for seven therapies and ranged between 30 and 70 weeks. Significant differences in the pre- versus post-treatment annualized relapse rate were present for all therapies apart from intramuscular interferon beta-1a. In conclusion we have developed, and externally validated, a method to objectively quantify the duration of therapeutic lag on relapses and disability progression in different therapies in patients more than 3 years from multiple sclerosis onset. Objectively defined periods of expected therapeutic lag allows insights into the evaluation of treatment response in randomized clinical trials and may guide clinical decision-making in patients who experience early on-treatment disease activity. This method will subsequently be applied in studies that evaluate the effect of patient and disease characteristics on therapeutic lag.

Efficiency of Electropumping in Nanochannels.

Electropumping has been shown to be an effective means of inducing a net positive flow in fluids confined within planar nanochannels and carbon nanotubes. In this Letter, we investigate the efficiency of electropumping relative to Couette and Poiseuille flows. We apply a spatially uniform rotating electric field to a fluid confined in a functionalized nanochannel that couples the water's permanent dipole moment resulting in a net positive flow. We then induce a net positive flow in nanochannels for Couette and Poiseuille flows, matching volume flow rates to allow a direct comparison of average power dissipation per unit volume between all flow types. We show that while electropumping is less efficient than Couette flow, it is 4 orders of magnitude more efficient than Poiseuille flow. This suggests that, rather than being a mere novelty, electropumping is a far more energetically efficient means of transporting water compared to conventional pressure driven pumping.

Enhancing oncolytic virotherapy: Observations from a Voronoi Cell-Based model.

Oncolytic virotherapy is a promising cancer treatment using genetically modified viruses. Unfortunately, virus particles rapidly decay inside the body, significantly hindering their efficacy. In this article, treatment perturbations that could overcome obstacles to oncolytic virotherapy are investigated through the development of a Voronoi Cell-Based model (VCBM). The VCBM derived captures the interaction between an oncolytic virus and cancer cells in a 2-dimensional setting by using an agent-based model, where cell edges are designated by a Voronoi tessellation. Here, we investigate the sensitivity of treatment efficacy to the configuration of the treatment injections for different tumour shapes: circular, rectangular and irregular. The model predicts that multiple off-centre injections improve treatment efficacy irrespective of tumour shape. Additionally, we investigate delaying the infection of cancer cells by modifying viral particles with a substance such as alginate (a hydrogel polymer used in a range of cancer treatments). Simulations of the VCBM show that delaying the infection of cancer cells, and thus allowing more time for virus dissemination, can improve the efficacy of oncolytic virotherapy. The simulated treatment noticeably decreases the tumour size with no increase in toxicity. Improving oncolytic virotherapy in this way allows for a more effective treatment without changing its fundamental essence.

Computation of the equilibrium three-particle entropy for dense atomic fluids by molecular dynamics simulation.

We have computed the two- and three-particle contribution to the entropy of a Weeks-Chandler-Andersen fluid via molecular dynamics simulations. The three-particle correlation function and entropy were computed with a new method which simplified the calculation. Results are qualitatively similar to Lennard-Jones systems. We observed a numerical instability in the three-particle contribution. This phenomenon has been previously detected when the traditional method is used; thus, it is likely to be intrinsic in the computation. While the effect of statistical fluctuations can be removed through an extrapolation procedure, the discretization error due to the finite bin size is more difficult to characterize. With a correct choice of the bin size, a good estimate of the three-particle entropy contribution can be achieved at any state, even close to the freezing point. We observed that, despite the fact that the magnitude of the three-particle contribution increases significantly compared to that of the two-particle contribution as freezing is approached, the error induced from overestimation of the excess entropy by the two- and three-body terms exceeds that induced by approximating the excess entropy with the two body term alone.

Inducing a Net Positive Flow of Water in Functionalized Concentric Carbon Nanotubes Using Rotating Electric Fields.

Electropumping has shown great potential as an effective means of inducing a net positive flow of water in confined channels. In this paper we present the first nonequilibrium molecular dynamics study and continuum based numerical solutions that demonstrate an effective net positive flow between concentric carbon nanotubes (CNT) using electropumping. We apply a spatially uniform rotating electric field that couples to the water's permanent dipole moment. Taking advantage of the coupling between the spin angular momentum and the linear momentum we break the symmetry of the channel radius by functionalizing the inner CNT's outer surface with carboxyl groups to induce a net positive flow. We also show that our results for concentric nanotubes are consistent with our previous work where we demonstrated that an increase in functionalization beyond an optimal point in a single walled carbon nanotube resulted in a decrease in positive net flow. We then numerically solve the coupled hydrodynamic momentum equations to show that the nonequilibrium molecular dynamics results are consistent with the continuum theory.

Oncolytic virotherapy for tumours following a Gompertz growth law.

Oncolytic viruses are genetically engineered to treat growing tumours and represent a very promising therapeutic strategy. Using a Gompertz growth law, we discuss a model that captures the in vivo dynamics of a cancer under treatment with an oncolytic virus. With the aid of local stability analysis and bifurcation plots, the typical interactions between virus and tumour are investigated. The system shows a singular equilibrium and a number of nonlinear behaviours that have interesting biological consequences, such as long-period oscillations and bistable states where two different outcomes can occur depending on the initial conditions. Complete tumour eradication appears to be possible only for parameter combinations where viral characteristics match well with the tumour growth rate. Interestingly, the model shows that therapies with a high initial injection or involving a highly effective virus do not universally result in successful strategies for eradication. Further, the use of additional, "boosting" injection schedules does not always lead to complete eradication. Our framework, instead, suggests that low viral loads can be in some cases more effective than high loads, and that a less resilient virus can help avoid high amplitude oscillations between tumours and virus. Finally, the model points to a number of interesting findings regarding the role of oscillations and bistable states between a tumour and an oncolytic virus. Strategies for the elimination of such fluctuations depend strongly on the initial viral load and the combination of parameters describing the features of the tumour and virus.

Effects of mutations and immunogenicity on outcomes of anti-cancer therapies for secondary lesions.

Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to express a variety of competing phenotypes with different attributes and thus respond differently to various anti-cancer therapies. In this paper, a mathematical framework incorporating a system of delay differential equations for the immune system activation cycle and an agent-based approach for tumour-immune interaction is presented. The focus is on those metastatic, secondary solid lesions that are still undetected and non-vascularised. By using available experimental data, we analyse the effects of combination therapies on these lesions and investigate the role of mutations on the rates of success of common treatments. Findings show that mutations, growth properties and immunoediting influence therapies' outcomes in nonlinear and complex ways, affecting cancer lesion morphologies, phenotypical compositions and overall proliferation patterns. Cascade effects on final outcomes for secondary lesions are also investigated, showing that actions on primary lesions could sometimes result in unexpected clearances of secondary tumours. This outcome is strongly dependent on the clonal composition of the primary and secondary masses and is shown to allow, in some cases, the control of the disease for years.

Stability and Hopf bifurcation analysis for a Lac operon model with nonlinear degradation rate and time delay.

In this paper, we construct a discrete time delay Lac operon model with nonlinear degradation rate for mRNA, resulting from the interaction among several identical mRNA pieces. By taking a discrete time delay as bifurcation parameter, we investigate the nonlinear dynamical behaviour arising from the model, using mathematical tools such as stability and bifurcation theory. Firstly, we discuss the existence and uniqueness of the equilibrium for this system and investigate the effect of discrete delay on its dynamical behaviour. Absence or limited delay causes the system to have a stable equilibrium, which changes into a Hopf point producing oscillations if time delay is increased. These sustained oscillation are shown to be present only if the nonlinear degradation rate for mRNA satisfies specific conditions. The direction of the Hopf bifurcation giving rise to such oscillations is also determined, via the use of the so-called multiple time scales technique. Finally, numerical simulations are shown to validate and expand the theoretical analysis. Overall, our findings suggest that the degree of nonlinearity of the model can be used as a control parameter for the stabilisation of the system.

HPV Screening and Vaccination Strategies in an Unscreened Population: A Mathematical Modeling Study.

Human papillomavirus (HPV), a sexually transmitted infection, is the necessary cause of cervical cancer, the third most common cancer affecting women worldwide. Prevention and control strategies include vaccination, screening, and treatment. While HPV prevention and control efforts are important worldwide, they are especially important in low-income areas with a high infection rate or high rate of cervical cancer. This study uses mathematical modeling to explore various vaccination and treatment strategies to control for HPV and cervical cancer while using Nepal as a case study. Two sets of deterministic models were created with the goal of understanding the impact of various prevention and control strategies. The first set of models examines the relative importance of screening and vaccination in an unscreened population, while the second set examines various screening scenarios. Partial rank correlation coefficients confirm the importance of screening and treatment in the reduction of HPV infections and cancer cases even when vaccination uptake is high. Results also indicate that less expensive screening technologies can achieve the same overall goal as more expensive screening technologies.

Infection-acquired versus vaccine-acquired immunity in an SIRWS model.

In some disease systems, the process of waning immunity can be subtle, involving a complex relationship between the duration of immunity-acquired either through natural infection or vaccination-and subsequent boosting of immunity through asymptomatic re-exposure. We present and analyse a model of infectious disease transmission where primary and secondary infections are distinguished to examine the interplay between infection and immunity. Additionally we allow the duration of infection-acquired immunity to differ from that of vaccine-acquired immunity to explore the impact on long-term disease patterns and prevalence of infection in the presence of immune boosting. Our model demonstrates that vaccination may induce cyclic behaviour, and the ability of vaccinations to reduce primary infections may not lead to decreased transmission. Where the boosting of vaccine-acquired immunity delays a primary infection, the driver of transmission largely remains primary infections. In contrast, if the immune boosting bypasses a primary infection, secondary infections become the main driver of transmission under a sufficiently long duration of immunity. Our results show that the epidemiological patterns of an infectious disease may change considerably when the duration of vaccine-acquired immunity differs from that of infection-acquired immunity. Our study highlights that for any particular disease and associated vaccine, a detailed understanding of the waning and boosting of immunity and how the duration of protection is influenced by infection prevalence are important as we seek to optimise vaccination strategies.

A model of the effects of cancer cell motility and cellular adhesion properties on tumour-immune dynamics.

We present a three-dimensional model simulating the dynamics of an anti-cancer T-cell response against a small, avascular, early-stage tumour. Interactions at the tumour site are accounted for using an agent-based model (ABM), while immune cell dynamics in the lymph node are modelled as a system of delay differential equations (DDEs). We combine these separate approaches into a two-compartment hybrid ABM-DDE system to capture the T-cell response against the tumour. In the ABM at the tumour site, movement of tumour cells is modelled using effective physical forces with a specific focus on cell-to-cell adhesion properties and varying levels of tumour cell motility, thus taking into account the ability of cancer cells to spread and form clusters. We consider the effectiveness of the immune response over a range of parameters pertaining to tumour cell motility, cell-to-cell adhesion strength and growth rate. We also investigate the dependence of outcomes on the distribution of tumour cells. Low tumour cell motility is generally a good indicator for successful tumour eradication before relapse, while high motility leads, almost invariably, to relapse and tumour escape. In general, the effect of cell-to-cell adhesion on prognosis is dependent on the level of tumour cell motility, with an often unpredictable cross influence between adhesion and motility, which can lead to counterintuitive effects. In terms of overall tumour shape and structure, the spatial distribution of cancer cells in clusters of various sizes has shown to be strongly related to the likelihood of extinction.

Molecular simulation of the thermodynamic, structural, and vapor-liquid equilibrium properties of neon.

The thermodynamic, structural, and vapor-liquid equilibrium properties of neon are comprehensively studied using ab initio, empirical, and semi-classical intermolecular potentials and classical Monte Carlo simulations. Path integral Monte Carlo simulations for isochoric heat capacity and structural properties are also reported for two empirical potentials and one ab initio potential. The isobaric and isochoric heat capacities, thermal expansion coefficient, thermal pressure coefficient, isothermal and adiabatic compressibilities, Joule-Thomson coefficient, and the speed of sound are reported and compared with experimental data for the entire range of liquid densities from the triple point to the critical point. Lustig's thermodynamic approach is formally extended for temperature-dependent intermolecular potentials. Quantum effects are incorporated using the Feynman-Hibbs quantum correction, which results in significant improvement in the accuracy of predicted thermodynamic properties. The new Feynman-Hibbs version of the Hellmann-Bich-Vogel potential predicts the isochoric heat capacity to an accuracy of 1.4% over the entire range of liquid densities. It also predicts other thermodynamic properties more accurately than alternative intermolecular potentials.

Periodic solutions in an SIRWS model with immune boosting and cross-immunity.

Incidence of whooping cough, an infection caused by Bordetella pertussis and Bordetella parapertussis, has been on the rise since the 1980s in many countries. Immunological interactions, such as immune boosting and cross-immunity between pathogens, have been hypothesised to be important drivers of epidemiological dynamics. We present a two-pathogen model of transmission which examines how immune boosting and cross-immunity can influence the timing and severity of epidemics. We use a combination of numerical simulations and bifurcation techniques to study the dynamical properties of the system, particularly the conditions under which stable periodic solutions are present. We derive analytic expressions for the steady state of the single-pathogen model, and give a condition for the presence of periodic solutions. A key result from our two-pathogen model is that, while studies have shown that immune boosting at relatively strong levels can independently generate periodic solutions, cross-immunity allows for the presence of periodic solutions even when the level of immune boosting is weak. Asymmetric cross-immunity can produce striking increases in the incidence and period. Our study underscores the importance of developing a better understanding of the immunological interactions between pathogens in order to improve model-based interpretations of epidemiological data.