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 Bulletin of Mathematical BiologyJournal Prestige (SJR): 0.717 Citation Impact (citeScore): 1Number of Followers: 9      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1522-9602 - ISSN (Online) 0092-8240 Published by Springer-Verlag  [2467 journals]
• Reframing Optimal Control Problems for Infectious Disease Management in
Low-Income Countries

Abstract: Abstract Optimal control theory can be a useful tool to identify the best strategies for the management of infectious diseases. In most of the applications to disease control with ordinary differential equations, the objective functional to be optimized is formulated in monetary terms as the sum of intervention costs and the cost associated with the burden of disease. We present alternate formulations that express epidemiological outcomes via health metrics and reframe the problem to include features such as budget constraints and epidemiological targets. These alternate formulations are illustrated with a compartmental cholera model. The alternate formulations permit us to better explore the sensitivity of the optimal control solutions to changes in available budget or the desired epidemiological target. We also discuss some limitations of comprehensive cost assessment in epidemiology.
PubDate: 2023-03-12

• The Impact of Host Abundance on the Epidemiology of Tick-Borne Infection

Abstract: Abstract Tick-borne diseases are an increasing global public health concern due to an expanding geographical range and increase in abundance of tick-borne infectious agents. A potential explanation for the rising impact of tick-borne diseases is an increase in tick abundance which may be linked to an increase in density of the hosts on which they feed. In this study, we develop a model framework to understand the link between host density, tick demography and tick-borne pathogen epidemiology. Our model links the development of specific tick stages to the specific hosts on which they feed. We show that host community composition and host density have an impact on tick population dynamics and that this has a consequent impact on host and tick epidemiological dynamics. A key result is that our model framework can exhibit variation in host infection prevalence for a fixed density of one host type due to changes in density of other host types that support different tick life stages. Our findings suggest that host community composition may play a crucial role in explaining the variation in prevalence of tick-borne infections in hosts observed in the field.
PubDate: 2023-03-09

• Boolean Models of the Transport, Synthesis, and Metabolism of Tryptophan
in Escherichia coli

Abstract: Abstract The tryptophan (trp) operon in Escherichia coli codes for the proteins responsible for the synthesis of the amino acid tryptophan from chorismic acid, and has been one of the most well-studied gene networks since its discovery in the 1960s. The tryptophanase (tna) operon codes for proteins needed to transport and metabolize it. Both of these have been modeled individually with delay differential equations under the assumption of mass-action kinetics. Recent work has provided strong evidence for bistable behavior of the tna operon. The authors of Orozco-Gómez et al. (Sci Rep 9(1):5451, 2019) identified a medium range of tryptophan in which the system has two stable steady-states, and they reproduced these experimentally. In this paper, we will show how a Boolean model can capture this bistability. We will also develop and analyze a Boolean model of the trp operon. Finally, we will combine these two to create a single Boolean model of the transport, synthesis, and metabolism of tryptophan. In this amalgamated model, the bistability disappears, presumably reflecting the ability of the trp operon to produce tryptophan and drive the system toward homeostasis. All of these models have longer attractors that we call “artifacts of synchrony”, which disappear in the asynchronous automata. This curiously matches the behavior of a recent Boolean model of the arabinose operon in E. coli, and we discuss some open-ended questions that arise along these lines.
PubDate: 2023-03-06

• Coevolutionary Dynamics of Host Immune and Parasite Virulence Based on an
Age-Structured Epidemic Model

Abstract: Abstract Hosts can activate a defensive response to clear the parasite once being infected. To explore how host survival and fecundity are affected by host-parasite coevolution for chronic parasitic diseases, in this paper, we proposed an age-structured epidemic model with infection age, in which the parasite transmission rate and parasite-induced mortality rate are structured by the infection age. By use of critical function analysis method, we obtained the existence of the host immune evolutionary singular strategy which is a continuous singular strategy (CSS). Assume that parasite-induced mortality begins at infection age $$\tau$$ and is constant v thereafter. We got that the value of the CSS, $$c^*$$ , monotonically decreases with respect to infection age $$\tau$$ (see Case (I)), while it is non-monotone if the constant v positively depends on the immune trait c (see Case (II)). This non-monotonicity is verified by numerical simulations and implies that the direction of immune evolution depends on the initial value of immune trait. Besides that, we adopted two special forms of the parasite transmission rate to study the parasite’s virulence evolution, by maximizing the basic reproduction ratio $${\mathcal {R}}_0$$ . The values of the convergence stable parasite’s virulence evolutionary singular strategies $$v^*$$ and $$k^*$$ increase monotonically with respect to time lag L (i.e., the time lag between the onset of transmission and mortality). At the singular strategy $$v^*$$ and $$k^*$$ , we further obtained the expressions of the case mortalities $$\chi ^*$$ and how they are affected by the time lag L. Finally, we only presented some preliminary results about host and parasite coevolution dynamics, including a general condition under which the coevolutionary singular strategy $$(c^*,v^*)$$ is evolutionarily stable.
PubDate: 2023-02-28

• Correction to: Coupling the Within-Host Process and Between-Host
Transmission of COVID-19 Suggests Vaccination and School Closures are
Critical

PubDate: 2023-02-26

• Simulation of Angiogenesis in Three Dimensions: Development of the Retinal
Circulation

Abstract: Abstract A theoretical model is used to describe the three-dimensional development of the retinal circulation in the human eye, which occurs after the initial spread of vasculature across the inner surface of the retina. In the model, random sprouting angiogenesis is driven by a growth factor that is produced in tissue at a rate dependent on oxygen level and diffuses to existing vessels. Vessel sprouts connect to form pathways for blood flow and undergo remodeling and pruning. These processes are controlled by known or hypothesized vascular responses to hemodynamic and biochemical stimuli, including conducted responses along vessel walls. The model shows regression of arterio-venous connections on the surface of the retina, allowing perfusion of the underlying tissue. A striking feature of the retinal circulation is the formation of two vascular plexuses located at the inner and outer surfaces of the inner nuclear layer within the retina. The model is used to test hypotheses regarding the formation of these structures. A mechanism based on local production and diffusion of growth factor is shown to be ineffective. However, sprout guidance by localized structures on the boundaries of the inner nuclear layer can account for plexus formation. The resulting networks have vascular density, perfusion and oxygen transport characteristics consistent with observed properties. The model shows how stochastic generation of vascular sprouts combined with a set of biologically based response mechanisms can lead to the generation of a specialized three-dimensional vascular structure with a high degree of organization.
PubDate: 2023-02-26

• Reading Frame Retrieval of Genes: A New Parameter of Codon Usage Based on
the Circular Code Theory

Abstract: Abstract Based on the circular code theory, we define a new function f that quantifies the property of reading frame retrieval (RFR) of genes from their codon usage. This RFR function f is computed on a massive scale in genes of genomes of bacteria, eukaryotes and archaea. By expressing f as a function of the mean number  $$\overline{n}$$ of codons per gene, a “universal” property is identified, whatever the kingdom: the reading frame retrieval is enhanced in large genes. By investigating this property according to the theory developed, a Spearman’s rank correlation with a strong negative coefficient is observed between the codon usage dispersion d (from the uniform codon distribution  $$\frac{1}{64}$$ ) and the RFR function f, whatever the kingdom (p-values  $$<10^{-180}$$ in bacteria,  $$<10^{-61}$$ in eukaryotes and  $$<10^{-159}$$ in archaea). Thus, the reading frame retrieval is enhanced with the codon usage dispersion. Furthermore, this approach identifies a “genome centre” from which emerge two distinct “genome arms”: an upper arm and a lower arm, respectively, above and below the linear regression. The RFR function by itself or combined with classical methods (alignment, phylogeny) could also be a new approach to classify the genomes in the future.
PubDate: 2023-02-24

• Effects of Elasticity on Cell Proliferation in a Tissue-Engineering
Scaffold Pore

Abstract: Abstract Scaffolds engineered for in vitro tissue engineering consist of multiple pores where cells can migrate along with nutrient-rich culture medium. The presence of the nutrient medium throughout the scaffold pores promotes cell proliferation, and this process depends on several factors such as scaffold geometry, nutrient medium flow rate, shear stress, cell-scaffold focal adhesions and elastic properties of the scaffold material. While numerous studies have addressed the first four factors, the mathematical approach described herein focuses on cell proliferation rate in elastic scaffolds, under constant flux of nutrients. As cells proliferate, the scaffold pores radius shrinks and thus, in order to sustain the nutrient flux, the inlet applied pressure on the upstream side of the scaffold pore must be increased. This results in expansion of the elastic scaffold pore, which in turn further increases the rate of cell proliferation. Considering the elasticity of the scaffold, the pore deformation allows further cellular growth beyond that of inelastic conditions. In this paper, our objectives are as follows: (i) Develop a mathematical model for describing fluid dynamics, scaffold elasticity and cell proliferation for scaffolds consist of identical nearly cylindrical pores; (ii) Solve the models and then simulate cellular proliferation within an elastic pore. The simulation can emulate real life tissue growth in a scaffold and offer a solution which reduces the numerical burdens. Lastly, our results demonstrated are in qualitative agreement with experimental observations reported in the literature.
PubDate: 2023-02-24

• A Spatial Kinetic Model of Crowd Evacuation Dynamics with Infectious
Disease Contagion

Abstract: Abstract This paper proposes a kinetic theory approach coupling together the modeling of crowd evacuation from a bounded domain with exit doors and infectious disease contagion. The spatial movement of individuals in the crowd is modeled by a proper description of the interactions with people in the crowd and the environment, including walls and exits. At the same time, interactions among healthy and infectious individuals may generate disease spreading if exposure time is long enough. Immunization of the population and individual awareness to contagion is considered as well. Interactions are modeled by tools of game theory, that let us propose the so-called tables of games that are introduced in the general kinetic equations. The proposed model is qualitatively studied and, through a series of case studies, we explore different scenarios related to crowding and gathering formation within indoor venues under the spread of a respiratory infectious disease, obtaining insights on specific policies to reduce contagion that may be implemented.
PubDate: 2023-02-18

• Epicardial Dispersion of Repolarization Promotes the Onset of Reentry in
Brugada Syndrome: A Numerical Simulation Study

Abstract: Abstract The Brugada syndrome (BrS) is a cardiac arrhythmic disorder responsible for sudden cardiac death associated with the onset of ventricular arrhythmias, such as reentrant ventricular tachycardia and fibrillation. The mechanisms which lead to the onset of such electrical disorders in patients affected by BrS are not completely understood, yet. The aim of the present study is to investigate by means of numerical simulations the electrophysiological mechanisms at the basis of the morphology of electrocardiogram (ECG) and the onset of reentry associated with BrS. To this end, we consider the Bidomain equations coupled with the ten Tusscher–Panfilov membrane model, on an idealized wedge of human right ventricular tissue. The results have shown that: (1) epicardial dispersion of repolarization, generated by the coexistence of regions of early and late repolarization, due to different modulation of the $$I_\mathrm{{CaL}}$$ current, produces ECG waveforms exhibiting qualitatively the typical BrS morphology, characterized by ST elevation and partially negative T-waves; (2) epicardial dispersion of repolarization promotes the onset of reentry during the implementation of the programmed stimulation protocol, because of the conduction block occurring when a premature beat reaches the border of late repolarizing regions; and (3) the modulation of the $$I_\mathrm{{to}}$$ current affects the duration of reentry, which becomes sustained with a remarkable increase of $$I_\mathrm{{to}}$$ in the subepicardial layers.
PubDate: 2023-02-15

• RNA Secondary Structures with Given Motif Specification: Combinatorics and
Algorithms

Abstract: Abstract The study of native motifs of RNA secondary structures helps us better understand the formation and eventually the functions of these molecules. Commonly known structural motifs include helices, hairpin loops, bulges, interior loops, exterior loops and multiloops. However, enumerative results and generating algorithms taking into account the joint distribution of these motifs are sparse. In this paper, we present progress on deriving such distributions employing a tree-bijection of RNA secondary structures obtained by Schmitt and Waterman and a novel rake decomposition of plane trees. The key feature of the latter is that the derived components encode motifs of the RNA secondary structures without pseudoknots associated with the plane trees very well. As an application, we present an algorithm (RakeSamp) generating uniformly random secondary structures without pseudoknots that satisfy fine motif specifications on the length and degree of various types of loops as well as helices.
PubDate: 2023-02-13

• Modeling Syphilis and HIV Coinfection: A Case Study in the USA

Abstract: Abstract Syphilis and HIV infections form a dangerous combination. In this paper, we propose an epidemic model of HIV-syphilis coinfection. The model always has a unique disease-free equilibrium, which is stable when both reproduction numbers of syphilis and HIV are less than 1. If the reproduction number of syphilis (HIV) is greater than 1, there exists a unique boundary equilibrium of syphilis (HIV), which is locally stable if the invasion number of HIV (syphilis) is less than 1. Coexistence equilibrium exists and is stable when all reproduction numbers and invasion numbers are greater than 1. Using data of syphilis cases and HIV cases from the US, we estimated that both reproduction numbers for syphilis and HIV are slightly greater than 1, and the boundary equilibrium of syphilis is stable. In addition, we observed competition between the two diseases. Treatment for primary syphilis is more important in mitigating the transmission of syphilis. However, it might lead to increase of HIV cases. The results derived here could be adapted to other multi-disease scenarios in other regions.
PubDate: 2023-02-03

• Evaluation of the Relative Performance of the Subflattenings Method for
Phylogenetic Inference

Abstract: Abstract The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny—and by extension the complete tree—using pattern counts from a sequence alignment. The relatively small number of possible internal edges among a set of taxa (compared to the number of binary trees) makes these methods attractive; however, more could be done to evaluate their effectiveness for inferring phylogenetic trees. This is the case particularly for subflattenings, and the work we present here makes progress in this area. We introduce software for constructing and evaluating subflattenings for splits, utilising a number of methods to make computing subflattenings more tractable. We then present the results of simulations we have performed in order to compare the effectiveness of subflattenings to that of flattenings in terms of split score distributions, and susceptibility to possible biases. We find that subflattenings perform similarly to flattenings in terms of the distribution of split scores on the trees we examined, but may be less affected by bias arising from both split size/balance and long branch attraction. These insights are useful for developing effective algorithms to utilise these tools for the purpose of inferring phylogenetic trees.
PubDate: 2023-01-30

• On Parameter Identifiability in Network-Based Epidemic Models

Abstract: Abstract Modelling epidemics on networks represents an important departure from classical compartmental models which assume random mixing. However, the resulting models are high-dimensional and their analysis is often out of reach. It turns out that mean-field models, low-dimensional systems of differential equations, whose variables are carefully chosen expected quantities from the exact model provide a good approximation and incorporate explicitly some network properties. Despite the emergence of such mean-field models, there has been limited work on investigating whether these can be used for inference purposes. In this paper, we consider network-based mean-field models and explore the problem of parameter identifiability when observations about an epidemic are available. Making use of the analytical tractability of most network-based mean-field models, e.g. explicit analytical expressions for leading eigenvalue and final epidemic size, we set up the parameter identifiability problem as finding the solution or solutions of a system of coupled equations. More precisely, subject to observing/measuring growth rate and final epidemic size, we seek to identify parameter values leading to these measurements. We are particularly concerned with disentangling transmission rate from the network density. To do this, we give a condition for practical identifiability and we find that except for the simplest model, parameters cannot be uniquely determined, that is, they are practically unidentifiable. This means that there exist multiple solutions (a manifold of infinite measure) which give rise to model output that is close to the data. Identifying, formalising and analytically describing this problem should lead to a better appreciation of the complexity involved in fitting models with many parameters to data.
PubDate: 2023-01-27

• Correction to: Relation Between the Number of Peaks and the Number of
Reciprocal Sign Epistatic Interactions

PubDate: 2023-01-21

Variation in Host Tolerance

Abstract: Abstract While experimental studies have demonstrated within-population variation in host tolerance to parasitism, theoretical studies rarely predict for polymorphism to arise. However, most theoretical models do not consider the crucial distinction between tolerance to the effects of infection-induced deaths (mortality tolerance) and tolerance to the parasite-induced reduction in the reproduction of infected hosts (sterility tolerance). While some studies have examined trade-offs between host tolerance and resistance mechanisms, none has considered a correlation within different tolerance mechanisms. We assume that sterility tolerance and mortality tolerance are directly traded-off in a host population subjected to a pathogen and use adaptive dynamics to study their evolutionary behaviour. We find that such a trade-off between the two tolerance strategies can drive the host population to branch into dimorphic strains, leading to coexistence of strains with sterile hosts that have low mortality and fully fertile with high mortality rates. Further, we find that a wider range of trade-off shapes allows branching at intermediate- or high-infected population size. Our other significant finding is that sterility tolerance is maximised (and mortality tolerance minimised) at an intermediate disease-induced mortality rate. Additionally, evolution entirely reverses the disease prevalence pattern corresponding to the recovery rate, compared to when no strategies evolve. We provide novel predictions on the evolutionary behaviour of two tolerance strategies concerning such a trade-off.
PubDate: 2023-01-20

• Asymptotic Analysis of Optimal Vaccination Policies

Abstract: Abstract Targeted vaccination policies can have a significant impact on the number of infections and deaths in an epidemic. However, optimising such policies is complicated, and the resultant solution may be difficult to explain to policy-makers and to the public. The key novelty of this paper is a derivation of the leading-order optimal vaccination policy under multi-group susceptible–infected–recovered dynamics in two different cases. Firstly, it considers the case of a small vulnerable subgroup in a population and shows that (in the asymptotic limit) it is optimal to vaccinate this group first, regardless of the properties of the other groups. Then, it considers the case of a small vaccine supply and transforms the optimal vaccination problem into a simple knapsack problem by linearising the final size equations. Both of these cases are then explored further through numerical examples, which show that these solutions are also directly useful for realistic parameter values. Moreover, the findings of this paper give some general principles for optimal vaccination policies which will help policy-makers and the public to understand the reasoning behind optimal vaccination programs in more generic cases.
PubDate: 2023-01-20

• Modeling and Global Sensitivity Analysis of Strategies to Mitigate
Covid-19 Transmission on a Structured College Campus

Abstract: Abstract In response to the COVID-19 pandemic, many higher educational institutions moved their courses on-line in hopes of slowing disease spread. The advent of multiple highly-effective vaccines offers the promise of a return to “normal” in-person operations, but it is not clear if—or for how long—campuses should employ non-pharmaceutical interventions such as requiring masks or capping the size of in-person courses. In this study, we develop and fine-tune a model of COVID-19 spread to UC Merced’s student and faculty population. We perform a global sensitivity analysis to consider how both pharmaceutical and non-pharmaceutical interventions impact disease spread. Our work reveals that vaccines alone may not be sufficient to eradicate disease dynamics and that significant contact with an infectious surrounding community will maintain infections on-campus. Our work provides a foundation for higher-education planning allowing campuses to balance the benefits of in-person instruction with the ability to quarantine/isolate infectious individuals.
PubDate: 2023-01-13

• Concentration-Dependent Domain Evolution in Reaction–Diffusion
Systems

Abstract: Abstract Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic modelling in developmental biology. Most work to date has considered prescribed domains evolving as given functions of time, but not the scenario of concentration-dependent dynamics, which is also highly relevant in a developmental setting. Here, we study such concentration-dependent domain evolution for reaction–diffusion systems to elucidate fundamental aspects of these more complex models. We pose a general form of one-dimensional domain evolution and extend this to N-dimensional manifolds under mild constitutive assumptions in lieu of developing a full tissue-mechanical model. In the 1D case, we are able to extend linear stability analysis around homogeneous equilibria, though this is of limited utility in understanding complex pattern dynamics in fast growth regimes. We numerically demonstrate a variety of dynamical behaviours in 1D and 2D planar geometries, giving rise to several new phenomena, especially near regimes of critical bifurcation boundaries such as peak-splitting instabilities. For sufficiently fast growth and contraction, concentration-dependence can have an enormous impact on the nonlinear dynamics of the system both qualitatively and quantitatively. We highlight crucial differences between 1D evolution and higher-dimensional models, explaining obstructions for linear analysis and underscoring the importance of careful constitutive choices in defining domain evolution in higher dimensions. We raise important questions in the modelling and analysis of biological systems, in addition to numerous mathematical questions that appear tractable in the one-dimensional setting, but are vastly more difficult for higher-dimensional models.
PubDate: 2023-01-13

• Breast Cancer Exosomal microRNAs Facilitate Pre-Metastatic Niche Formation
in the Bone: A Mathematical Model

Abstract: Abstract Pre-metastatic niche is a location where cancer cells, separating from a primary tumor, find “fertile soil” for growth and proliferation, ensuring successful metastasis. Exosomal miRNAs of breast cancer are known to enter the bone and degrade it, which facilitates cancer cells invasion into the bone interior and ensures its successful colonization. In this paper, we use a mathematical model to first describe, in health, the continuous remodeling of the bone by bone-forming osteoblasts, bone-resorbing osteoclasts and the RANKL-OPG-RANK signaling system, which keeps the balance between bone formation and bone resorption. We next demonstrate how breast cancer exosomal miRNAs disrupt this balance, either by increasing or by decreasing the ratio of osteoclasts/osteoblasts, which results in abnormal high bone resorption or abnormal high bone forming, respectively, and in bone weakening in both cases. Finally we consider the case of abnormally high resorption and evaluate the effect of drugs, which may increase bone density to normal level, thus protecting the bone from invasion by cancer cells.
PubDate: 2023-01-06
DOI: 10.1007/s11538-022-01117-0

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