Mathematical Biosciences最新文献

Vaping, or the use of electronic cigarettes (e-cigarettes), is an ongoing issue for public health. The rapid increase in e-cigarette usage, particularly among adolescents, has often been referred to as an epidemic. Drawing upon this epidemiological analogy between vaping and infectious diseases as a theoretical framework, we present a deterministic compartmental model of adolescent e-cigarette smoking which accounts for social influences on initiation, relapse, and cessation behaviours. We use results from a sensitivity analysis of the model’s parameters on various response variables to identify key influences on system dynamics and simplify the model into one that can be analysed more thoroughly. We identify a single feasible endemic equilibrium for the proportion of smokers that decreases as social influence on cessation increases. Through steady state and stability analyses, as well as simulations of the model, we conclude that social influences from and on temporary quitters are not important in overall model dynamics, and that social influences from permanent quitters can have a significant impact on long-term system dynamics. In particular, we show that social influence on cessation can induce persistent recurrent smoking outbreaks.

Human immunodeficiency virus (HIV) can persist in infected individuals despite prolonged antiretroviral therapy and it may spread through two modes: virus-to-cell and cell-to-cell transmissions. Understanding viral infection dynamics is pivotal for elucidating HIV pathogenesis. In this study, we incorporate the loss term of virions, and both virus-to-cell and cell-to-cell infection modes into a within-host HIV model, which also takes into consideration the proliferation of healthy target cells stimulated by free viruses. By constructing suitable Lyapunov function and applying geometric methods, we establish global stability results of the infection free equilibrium and the infection persistent equilibrium, respectively. Our findings highlight the crucial role of the basic reproduction number in the threshold dynamics. Moreover, we use the loss rate of virions as the bifurcation parameter to investigate stability switches of the positive equilibrium, local Hopf bifurcation, and its global continuation. Numerical simulations validate our theoretical results, revealing rich viral dynamics including backward bifurcation, saddle–node bifurcation, and bistability phenomenon in the sense that the infection free equilibrium and a limit cycle are both locally asymptotically stable. These insights contribute to a deeper understanding of HIV dynamics and inform the development of effective therapeutic strategies.

The Sterile Insect Technique (SIT) is one of the sustainable strategies for the control of disease vectors, which consists of releasing sterilized males that will mate with the wild females, resulting in a reduction and, eventually a local elimination, of the wild population. The implementation of the SIT in the field can become problematic when there are inaccessible areas where the release of sterile insects cannot be carried out directly, and the migration of wild insects from these areas to the treated zone may influence the efficacy of this technique. However, we can also take advantage of the movement of sterile individuals to control the wild population in these unreachable places. In this paper, we derive a two-patch model for Aedes mosquitoes where we consider the discrete diffusion between the treated area and the inaccessible zone. We investigate two different release strategies (constant and impulsive periodic releases), and by using the monotonicity of the model, we show that if the number of released sterile males exceeds some threshold, the technique succeeds in driving the whole population in both areas to extinction. This threshold depends on not only the biological parameters of the population but also the diffusion between the two patches.

Polymicrobial infections, caused by a community of multiple micro-organisms, are often associated with increased infection severity and poorer patient outcomes. The design of improved antimicrobial treatment strategies for PMIs can be supported by an understanding of their ecological and evolutionary dynamics. Bacterial species present in polymicrobial infections can produce virulence factors to inhibit host immune responses, such as neutrophil recruitment and phagocytosis. The presence of virulence factors can indirectly affect other bacterial species acting as a type of host-mediated interspecies interaction. The aim of this study was to assess how bacterial virulence factors targeting neutrophil function influence ecology and treatment outcomes of PMIs. An agent-based model was constructed which describes a dual-species bacterial population in the presence of neutrophils and a bacteriostatic drug. Our analysis has revealed unforeseen dynamics of the interplay of multiple virulence factors acting as interspecies interaction. We found that the distribution of two phagocytosis-inhibiting virulence factors amongst species can impact whether they have a mutually protective effect for both species. The addition of a virulence factor inhibiting neutrophil recruitment was found to reduce the protective effect of phagocytosis-inhibiting virulence factors. Furthermore we demonstrate the importance of virulence strength of a species relative to other virulent species to determine the fate of a species. We conclude that virulence factors are an important driver of population dynamics in polymicrobial infections, and may be a relevant therapeutic target for treatment of polymicrobial infections.

A new mathematical model of melatonin synthesis in pineal cells is created and connected to a slightly modified previously created model of the circadian clock in the suprachiasmatic nucleus (SCN). The SCN influences the production of melatonin by upregulating two key enzymes in the pineal. The melatonin produced enters the blood and the cerebrospinal fluid and thus the SCN, influencing the circadian clock. We show that the model of melatonin synthesis corresponds well with extant experimental data and responds similarly to clinical experiments on bright light in the middle of the night. Melatonin is widely used to treat jet lag and sleep disorders. We show how the feedback from the pineal to the SCN causes phase resetting of the circadian clock. Melatonin doses early in the evening advance the clock and doses late at night delay the clock with a dead zone in between where the phase of the clock does not change.

Macrophages are a type of white blood cell that play a significant role in determining the inflammatory response associated with a wide range of medical conditions. They are highly plastic, having the capacity to adopt numerous polarisation states or ‘phenotypes’ with disparate pro- or anti-inflammatory roles. Many previous studies divide macrophages into two categorisations: M1 macrophages are largely pro-inflammatory in nature, while M2 macrophages are largely restorative. However, there is a growing body of evidence that the M1 and M2 classifications represent the extremes of a much broader spectrum of phenotypes, and that intermediate phenotypes can play important roles in the progression or treatment of many medical conditions. In this article, we present a model of macrophage dynamics that includes a continuous description of phenotype, and hence incorporates intermediate phenotype configurations. We describe macrophage phenotype switching via nonlinear convective flux terms that scale with background levels of generic pro- and anti-inflammatory mediators. Through numerical simulation and bifurcation analysis, we unravel the model’s resulting dynamics, paying close attention to the system’s multistability and the extent to which key macrophage–mediator interactions provide bifurcations that act as switches between chronic states and restoration of health. We show that interactions that promote M1-like phenotypes generally result in a greater array of stable chronic states, while interactions that promote M2-like phenotypes can promote restoration of health. Additionally, our model admits oscillatory solutions reminiscent of relapsing–remitting conditions, with macrophages being largely polarised toward anti-inflammatory activity during remission, but with intermediate phenotypes playing a role in inflammatory flare-ups. We conclude by reflecting on our observations in the context of the ongoing pursuance of novel therapeutic interventions.

The cell division cycle is a fundamental physiological process displaying a great degree of plasticity during the course of multicellular development. This plasticity is evident in the transition from rapid and stringently-timed divisions of the early embryo to subsequent size-controlled mitotic cycles. Later in development, cells may pause and restart proliferation in response to myriads of internal or external signals, or permanently exit the cell cycle following terminal differentiation or senescence. Beyond this, cells can undergo modified cell division variants, such as endoreplication, which increases their ploidy, or meiosis, which reduces their ploidy. This wealth of behaviours has led to numerous conceptual analogies intended as frameworks for understanding the proliferative program. Here, we aim to unify these mechanisms under one dynamical paradigm. To this end, we take a control theoretical approach to frame the cell cycle as a pair of arrestable and mutually-inhibiting, doubly amplified, negative feedback oscillators controlling chromosome replication and segregation events, respectively. Under appropriate conditions, this framework can reproduce fixed-period oscillations, checkpoint arrests of variable duration, and endocycles. Subsequently, we use phase plane and bifurcation analysis to explain the dynamical basis of these properties. Then, using a physiologically realistic, biochemical model, we show that the very same regulatory structure underpins the diverse functions of the cell cycle control network. We conclude that Newton's cradle may be a suitable mechanical analogy of how the cell cycle is regulated.

In the wake of epidemics, quarantine measures are typically recommended by health authorities or governments to help control the spread of the disease. Compared with mandatory quarantine, voluntary quarantine offers individuals the liberty to decide whether to isolate themselves in case of infection exposure, driven by their personal assessment of the trade-off between economic loss and health risks as well as their own sense of social responsibility and concern for public health. To better understand self-motivated health behavior choices under these factors, here we incorporate voluntary quarantine into an endemic disease model – the susceptible–infected–susceptible (SIS) model – and perform comprehensive agent-based simulations to characterize the resulting behavior-disease interactions in structured populations. We quantify the conditions under which voluntary quarantine will be an effective intervention measure to mitigate disease burden. Furthermore, we demonstrate how individual decision-making factors, including the level of temptation to refrain from quarantine and the degree of social compassion, impact compliance levels of voluntary quarantines and the consequent collective disease mitigation efforts. We find that successful disease control requires either a sufficiently low level of temptation or a sufficiently high degree of social compassion, such that even complete containment of the epidemic is attainable. In addition to well-mixed populations, we have also analyzed other more realistic social networks of contacts, including spatial lattices, small-world networks, and real social networks. Our work offers new insights into the fundamental social dilemma aspect of disease control through non-pharmaceutical interventions, such as voluntary quarantine and isolation, where the collective outcome of individual decision-making is crucial.