Drugs of abuse, such as opiates, have been widely associated with diminishing host-immune responses, including suppression of HIV-specific antibody responses. In particular, periodic intake of the drugs of abuse can result in time-varying periodic antibody level within HIV-infected individuals, consequently altering the HIV dynamics. In this study, we develop a mathematical model to analyze the effects

The many variations on a graphic illustrating the impact of non-pharmaceutical measures to mitigate pandemic influenza that have appeared in recent news reports about COVID-19 suggest a need to better explain the mechanism by which social distancing reduces the spread of infectious diseases. And some reports understate one benefit of reducing the frequency or proximity of interpersonal encounters,

Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition for absolute delay stability of equilibrium concentrations, i.e., local asymptotic stability independent of the delay parameters. Several interesting examples on sequestration

Stem cells in the bone marrow differentiate to ultimately become mature, functioning blood cells through a tightly regulated process (hematopoiesis) including a stem cell niche interaction and feedback through the immune system. Mutations in a hematopoietic stem cell can create a cancer stem cell leading to a less controlled production of malfunctioning cells in the hematopoietic system. This was mathematically

The emerging coronavirus SARS-CoV-2 has caused a COVID-19 pandemic. SARS-CoV-2 causes a generally mild, but sometimes severe and even life-threatening infection, known as COVID-19. Currently, there exist no effective vaccines or drugs and, as such, global public authorities have so far relied upon non pharmaceutical interventions (NPIs). Since COVID-19 symptoms are aspecific and may resemble a common

Macrophage migration inhibitory factor (MIF) is a pleiotropic cytokine produced by immune cells; it can play a protective or deleterious role in response to pathogens. The intracellular malaria parasite secretes a similar protein, PMIF. The present paper is concerned with severe malarial anemia (SMA), where MIF suppresses the recruitment of red blood cells (RBCs) from the spleen and the bone marrow

During the templated biopolymerization processes of transcription and translation, a macromolecular machine, either an RNA polymerase or a ribosome, binds to a specific site on the template. Due to the sizes of these enzymes, there is a waiting time before one clears the binding site and another can bind. These clearance delays are relatively short, and one might think that they could be neglected

Malaria, a deadly infectious disease caused by the protozoan Plasmodium, remains a major public health menace affecting at least half the human race. Although the large-scale usage of insecticides-based control measures, notably long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS), have led to a dramatic reduction of the burden of this global scourge between the period 2000 to

Sanitary Emergency Measures (SEM) were implemented in Mexico on March 30th, 2020 requiring the suspension of non-essential activities. This action followed a Healthy Distance Sanitary action on March 23rd, 2020. The aim of both measures was to reduce community transmission of COVID-19 in Mexico by lowering the effective contact rate. Using a modification of the Kermack-McKendrick SEIR model we explore

Despite centuries of enormous control efforts, mosquito-borne diseases continue to show upward trend of morbidity. According to WHO reports, malaria caused 438000 deaths in the year 2015 and dengue cases have been increased 30-fold over the last five decades. To control these diseases, it is necessary to understand the transmission dynamics of them among mosquitoes. There are some vertically transmitted

A pandemic of a novel Coronavirus emerged in December of 2019 (COVID-19), causing devastating public health impact across the world. In the absence of a safe and effective vaccine or antivirals, strategies for controlling and mitigating the burden of the pandemic are focused on non-pharmaceutical interventions, such as social-distancing, contact-tracing, quarantine, isolation, and the use of face-masks

The reaction-diffusion equation is one of the possible ways for modeling animal movement, where the reactive part stands for the population growth and the diffusive part for random dispersal of the population. However, a reaction-diffusion model may not represent all aspects of the spatial dynamics, because of the existence of distinct mechanisms that can affect the movement, such as spatial memory

This paper deals with a stochastic SIR (Susceptible-Infected-Recovered) model with Erlang(k,μ) distributed infectious period commonly referred as SIkR model. We show that using the total number of remaining Erlang stages as the state variable, we do not need to keep track of the stages of individual infections, and can employ a first step analysis to efficiently obtain quantities of interest. We study

A key step in the origin of life is the emergence of a primitive metabolism. This requires the formation of a subset of chemical reactions that is both self-sustaining and collectively autocatalytic. A generic approach to study such processes ('RAF theory') has provided a precise and computationally effective way to address these questions, both on simulated data and in laboratory studies. In this

Infection of Herpes Simplex Virus type 2 (HSV-2) is a lifelong sexually transmitted disease. According to the Center for Disease Control and Prevention (CDC), 11.9% of the United States (U.S.) population was infected with HSV-2 in 2015-2016. The HSV-2 pathogen establishes latent infections in neural cells and can reactivate causing lesions later in life, a strategy that increases pathogenicity and

Trypanosoma rangeli (T. rangeli), a parasite, is not pathogenic to human but pathogenic to some vector species to induce the behavior changes of infected vectors and subsequently impact the transmission dynamics of other diseases such as Chagas disease which shares the same vector species. Here we develop a mathematical model and conduct qualitative analysis for the transmission dynamics of T. rangeli

In this work, we revisit the scaling analysis and commonly accepted conditions for the validity of the standard, reverse and total quasi-steady-state approximations through the lens of dimensional Tikhonov–Fenichel parameters and their respective critical manifolds. By combining Tikhonov–Fenichel parameters with scaling analysis and energy methods, we derive improved upper bounds on the approximation

An efficient method that assists in the re-parametrization of structurally unidentifiable models is introduced. It significantly reduces computational demand by combining numerical and symbolic identifiability calculations. This hybrid approach facilitates the re-parametrization of large unidentifiable ordinary differential equation models, including models where state transformations are required

In this paper we present a new method for deriving Itô stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same DCME, we prove that they are equivalent both in distribution, and in sample paths they produce. This allows us to formulate an algorithmic approach to deriving equivalent

Macrophages are one of the most important immune cell populations that can be found inside solid tumours. For a long time, it was thought that these cells have an anti-tumour role, but relatively recent research has shown that they can have both anti-tumour and pro-tumour roles as determined by their phenotypes. Due to the heterogeneity and plasticity of macrophage population, with cells changing their

We study mechanisms that can produce an increase of biomass production in batch processes when considering mixed cultures, compared to pure cultures. We show that growth thresholds or variable yields can produce 'overyielding', while this is not possible in the classical batch model with multiple species. We give sufficient conditions on the characteristics of the species to obtain overyielding, and

We consider a stochastic susceptible-infected-recovered (SIR) model with contact tracing on random trees and on the configuration model. On a rooted tree, where initially all individuals are susceptible apart from the root which is infected, we are able to find exact formulas for the distribution of the infectious period. Thereto, we show how to extend the existing theory for contact tracing in homogeneously

Several studies have been conducted to understand the dynamic of primary metabolisms in fruit by translating them into mathematics models. An ODE kinetic model of sugar metabolism has been developed by Desnoues et al. (2018) to simulate the accumulation of different sugars during peach fruit development. Two major drawbacks of this model are (a) the number of parameters to calibrate and (b) its integration

The phenomenon of chondrogenic pattern formation in the vertebrate limb is one of the best studied examples of organogenesis. Many different models, mathematical as well as conceptual, have been proposed for it in the last fifty years or so. In this review, we give a brief overview of the fundamental biological background, then describe in detail several models which aim to describe qualitatively and

In this study we present a mathematical model describing the transport of sodium in a fluid circulating in a counter-current tubular architecture, which constitutes a simplified model of Henle's loop in a kidney nephron. The model explicitly takes into account the epithelial layer at the interface between the tubular lumen and the surrounding interstitium. In a specific range of parameters, we show

Sensitivity analysis is an important part of a mathematical modeller's toolbox for model analysis. In this review paper, we describe the most frequently used sensitivity techniques, discussing their advantages and limitations, before applying each method to a simple model. Also included is a summary of current software packages, as well as a modeller's guide for carrying out sensitivity analyses. Finally

Metabolic networks are typically large, containing many metabolites and reactions. Dynamical models that aim to simulate such networks will consist of a large number of ordinary differential equations, with many kinetic parameters that must be estimated from experimental data. We assume these data to be metabolomics measurements made under steady-state conditions for different input fluxes. Assuming

An extended version of Birnbaum-Saunders distribution with five parameters is introduced. Theoretical aspects of five-parameter Birnbaum-Saunders distribution and the maximum likelihood estimation of parameters are presented. The reliability and applicability of the proposed distribution is evaluated using both simulation and real-world data namely bicoid gene expression profile. The findings of this

Delay differential equations are widely used in mathematical modeling to describe physical and biological systems, often inducing oscillatory behavior. In physiological systems, this instability may signify (i) an attempt to return to homeostasis or (ii) system dysfunction. In this study, we analyze a nonlinear, nonautonomous, nonhomogeneous open-loop neurological control model describing the autonomic

Phylogenetic trees are often constructed by using a metric on the set of taxa that label the leaves of the tree. While there are a number of methods for constructing a tree using a given metric, such trees will only display the metric if it satisfies the so-called "four point condition", established by Buneman in 1971. While this condition guarantees that a unique tree will display the metric, meaning

Volume 1, Issue 1 of Mathematical Biosciences was the venue for a now-classic paper on the application of singular perturbation theory in enzyme kinetics, "On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics" by F. G. Heineken, H. M. Tsuchiya and R. Aris. More than 50 years have passed, and yet this paper continues to be studied and mined for insights. This perspective

Does a high dispersal rate provide a competitive advantage when risking competitive exclusion? To this day, the theoretical literature cannot answer this question in full generality. The present paper focuses on the simplest mathematical model with two populations differing only in dispersal ability and whose one-dimensional territories are spatially segregated. Although the motion of the border between

Avian malaria is a mosquito-borne parasitic disease of birds caused by protists of the genera Plasmodium, most notably Plasmodium relictum. This disease has been identified as a primary cause of the drastic decline and extinctions of birds, in particular Hawaiian honeycreepers (Drepanidinae), where rates of mortality may exceed 90%. We formulate an epizootiological model of the transmission dynamics

Mathematical modelling is a useful technique to help elucidate the connection between non-transmural ischaemia and ST elevation and depression of the ECG. Generally, models represent non-transmural ischaemia using an ischaemic zone that extends from the endocardium partway to the epicardium. However, recent experimental work has suggested that ischaemia typically arises within the heart wall. This

Despite the wealth of empirical and theoretical studies, the origin and maintenance of cooperation is still an evolutionary riddle. In this context, ecological life-history traits which affect the efficiency of selection may play a role despite being often ignored. We consider here species such as bacteria, fungi, invertebrates and plants which exhibit resting stages in the form of a quiescent state

Historically, multi-state Markov models have been used to study breast cancer incidence and mammography screening effectiveness. In recent years, more biologically motivated continuous tumour growth models have emerged as alternatives. However, a number of challenges remain for these models to make use of the wealth of information available in large mammography cohort data. In particular, methodology

The cancer stem cell hypothesis states that tumors are heterogeneous and comprised of several different cell types that have a range of reproductive potentials. Cancer stem cells (CSCs), represent one class of cells that has both reproductive potential and the ability to differentiate. These cells are thought to drive the progression of aggressive and recurring cancers since they give rise to all other

Biological invasions have impacts on diverse social, ecological, and economic issues. Among others, invasion success can be determined by epidemiological aspects, intraspecific dynamics as, e.g., Allee effects, and interspecific interactions as, e.g., competition. In this study, a process-based model describing competitive eco-epidemiological dynamics of two species, which are both subject to an Allee

An efficient method for Bayesian model selection is presented for a broad class of continuous-time Markov chain models and is subsequently applied to two important problems in epidemiology. The first problem is to identify the shape of the infectious period distribution; the second problem is to determine whether individuals display symptoms before, at the same time, or after they become infectious

A system of partial differential equations is developed to describe the formation and clearance of amyloid β (Aβ) and the subsequent buildup of Aβ plaques in the brain, which are associated with Alzheimer's disease. The Aβ related proteins are divided into five distinct categories depending on their size. In addition to enzymatic degradation, the clearance via diffusion and the outflow of interstitial

Cooperating behaviors abound across all domains of life, but are vulnerable to invasion by cheaters. An important evolutionary question is to determine mechanisms that stabilize and maintain cooperation levels and prevent population collapse. Policing is one strategy populations may employ to achieve this goal, and it has been observed in many natural populations including microbes. Here we present

Fisheries management strategies in which large fish are selectively targeted and younger, smaller fish are protected can lead to disruption of stocks, truncation of the population size spectrum, and impaired recruitment. Balanced harvesting is an alternative approach, which distributes fishing mortality across a wide range of species and sizes in proportion to their natural productivity. Here, we investigate

Modeling a cell's response to encroaching ice has informed the development of cryopreservation protocols for four decades. It has been well documented that knowledge of the cellular state as a function of media and cooling rate faciliate informed cryopreservation protocol design and explain mechanisms of damage. However, previous efforts have neglected the interaction between solutes and the encroaching

One way to interject knowledge into clinically impactful forecasting is to use data assimilation, a nonlinear regression that projects data onto a mechanistic physiologic model, instead of a set of functions, such as neural networks. Such regressions have an advantage of being useful with particularly sparse, non-stationary clinical data. However, physiological models are often nonlinear and can have

In all complex organisms, the precise levels and timing of gene expression controls vital biological processes. In higher eukaryotes, including the fruit fly Drosophila melanogaster, the complex molecular control of transcription (the synthesis of RNA from DNA) and translation (the synthesis of proteins from RNA) events driving this gene expression are not fully understood. In particular, for Drosophila

When modeling a physical system using a Markov chain, it is often instructive to compute its probability distribution at statistical equilibrium, thereby gaining insight into the stationary, or long-term, behavior of the system. Computing such a distribution directly is problematic when the state space of the system is large. Here, we look at the case of a chemical reaction system that models the dynamics

Cell death-induced proliferation (CDIP) is a phenomenon in which cell death activates neighboring cells and promotes their proliferation. It was first reported as "compensatory proliferation" in injured tissues, which functions to maintain normal tissues. On the other hand, this phenomenon also affects potentially tumorigenic mutant cells and promotes tumorigenesis. This discrepancy may complicate

T-killer cells of the immune system eliminate virus-infected cells by releasing toxic granules through a direct cell to cell surface interface (synapse). The release of toxic granules only through the cell surface interface assures the specificity of the immune response. The toxic granule releasing apparatus, however, may not be aligned toward the synapse at the moment of the synapse formation. Therefore

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

The studies of mammalian vasculature are an essential part of biomedical research, enabling the development of physiological understanding and forming the background of medical techniques and therapy. Despite the fact that the basic principles of vessel network description were established in the first quarter of the twentieth century, a digital model describing the vasculature in full accordance with

We consider the problem of determining the time evolution of a trait distribution in a mathematical model of non-uniform populations with parametric heterogeneity. This means that we consider only heterogeneous populations in which heterogeneity is described by an individual specific parameter that differs in general from individual to individual, but does not change with time for the whole lifespan

A previous physiologically-structured model for a fish population based on individual-level characteristics is studied. The foraging rate is generalized to include a size-dependent functional response and the energy distribution of adults is generalized to permit both reproduction and growth. Equilibria are determined and their stability studied along with a discussion of harvesting strategies. The

As photoautotrophic microorganisms, microalgae feature complex mechanisms of photosynthesis and light energy transfer and as such studying their intrinsic growth kinetics is fairly difficult. In this article, the quantum yield of photochemical reaction was introduced in a study of microalgal kinetics to establish an intrinsic kinetic model of photoautotrophic microalgal growth. The blue-green algae

The total number of infections (epidemic size) and the time needed for the infection to go extinct (epidemic duration) represent two of the main indicators for the severity of infectious disease epidemics in human and livestock. However, few attempts have been made to address the problem of minimizing at the same time the epidemic size and duration from a theoretical point of view by using optimal

In recent times, several feature selection (FS) methods have introduced to identify the biomarkers from gene expression datasets. It has gained extensive attention to solve cancer classification problem, but they have some limitations. First, the majority of FS approaches increases the computational cost due to the centralized data structure. Second, an irrelevant ranked gene that could perform well

Cardiac ventricular tachycardia (VT) is a life-threatening arrhythmia consisting of a well organized structure of reentrant electrical excitation pathways. Understanding the generation and maintenance of the reentrant mechanisms, which lead to the onset of VT induced by premature beats in presence of infarct scar, is one of the most important issues in current electrocardiology. We investigate, by

By an extensive statistical analysis in genes of bacteria, archaea, eukaryotes, plasmids and viruses, a maximal C3-self-complementary trinucleotide circular code has been found to have the highest average occurrence in the reading frame of the ribosome during translation. Circular codes may play an important role in maintaining the correct reading frame. On the other hand, as several evolutionary theories

A kind of noncoding RNA with length more than 200 nucleotides named long noncoding RNA (lncRNA) has gained considerable attention in recent decades. Many studies have confirmed that human genome contains many thousands of lncRNAs. LncRNAs play significant roles in many important biological processes, including complex disease diagnosis, prognosis, prevention and treatment. For some important diseases

BACKGROUND The standard treatment for high-grade non-Hodgkin lymphoma involves the combination of chemotherapy and immunotherapy. We characterize in-silico the optimal combination protocol that maximizes the overall survival probability. We rely on a pharmacokinetics/pharmacodynamics (PK/PD) model that describes the joint evolution of tumor and effector cells, as well as the effects of both chemotherapy