Bulletin of Mathematical Biology

Alota, Cherrylyn P.; Pilar-Arceo, Carlene P. C.; de los Reyes V, Aurelio A.

doi: 10.1007/s11538-020-00769-0pmid: 32676740

Studies have been done using networks to represent the spread of infectious diseases in populations. For diseases with exposed individuals corresponding to a latent period, an SEIR model is formulated using an edge-based approach described by a probability generating function. The basic reproduction number is computed using the next generation matrix method and the final size of the epidemic is derived analytically. The SEIR model in this study is used to investigate the stochasticity of the SEIR dynamics. The stochastic simulations are performed applying continuous-time Gillespie’s algorithm given Poisson and power law with exponential cut-off degree distributions. The resulting predictions of the SEIR model given the initial conditions match well with the stochastic simulations, validating the accuracy of the SEIR model. We varied the contribution of the disease parameters and the average degree of the network in order to investigate their effects on the spread of disease. We verified that the infection and the recovery rates show significant effects on the dynamics of the disease transmission. While the exposed rate delays the spread of the disease, increasing it towards infinity would lead to almost the same dynamics as that of an SIR case. A network with high average degree results to an early and higher peak of the epidemic compared to a network with low average degree. The results in this paper can be used as an alternative way of explaining the spread of disease and it provides implications on the control strategies applied to mitigate the disease transmission.

Verma, Nitu; Verma, Babita K.; Pushpavanam, S.

doi: 10.1007/s11538-020-00763-6pmid: 32638157

In many oviparous species, the incubation temperature of the egg determines the sex of the offspring. This is known as temperature-dependent sex determination (TSD). The probability of the hatched offspring being male or female varies across the incubation temperature range. This leads to the appearance of different TSD patterns in species such as FM pattern where females are predominately born at lower temperature and males at higher temperature, FMF pattern where the probability of female being born is higher at extreme temperatures and of the male being born is high at intermediate temperatures. We analyze an enzymatic reaction system proposed in the literature involving sex hormones with positive feedback effect to understand the emergence of different TSD patterns. The nonlinearity in the model is accounted through temperature sensitivity of the reaction rates affecting the catalytic mechanism in the reaction system. We employ a dynamical systems approach of singularity theory and bifurcation analysis to divide the parameter plane of temperature sensitivities into different regions where different TSD patterns are observed. Bifurcation analysis in association with the delineation of the parameter space for different TSD pattern has led to the identification of a subspace where all the TSD patterns observed in nature can be realized. We also show how modulation of the sex hormone in the species can be used to change the probability of occurrence of a specific sex, thereby preventing the extinction of endangered species.

Al Basir, Fahad; Adhurya, Sagar; Banerjee, Malay; Venturino, Ezio; Ray, Santanu

doi: 10.1007/s11538-020-00767-2pmid: 32676825

Most of the plant viral diseases spread through vectors. In case of the persistently transmitted disease, there is a latent time of infection inside the vector after acquisition of the virus from the infected plant. Again, the plant after getting infectious agent shows an incubation time after the interaction with an infected vector before it becomes diseased. The goal of this work is to study the effect of both incubation delay and latent time on the dynamics of plant disease, and accordingly a delayed model has been proposed. The existence of the equilibria, basic reproductive number (R0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {R}_0$$\end{document}) and stability of equilibria have been studied. This study shows the relevance of the presence of two time delays, which may lead to system stabilization.

Pharaon, Joe; Bauch, Chris T.

doi: 10.1007/s11538-020-00762-7pmid: 32613297

Pre-exposure prophylaxis (PrEP) has been shown to be highly effective in reducing the risk of HIV infection in gay and bisexual men who have sex with men (GbMSM). However, PrEP does not protect against other sexually transmitted infections (STIs). In some populations, PrEP has also led to riskier behavior such as reduced condom usage, with the result that the prevalence of bacterial STIs like gonorrhea has increased. Here, we develop a compartmental model of the transmission of HIV and gonorrhea and the impacts of PrEP, condom usage, STI testing frequency and potential changes in sexual risk behavior stemming from the introduction of PrEP in a population of GbMSM. We find that introducing PrEP causes an increase in gonorrhea prevalence for a wide range of parameter values, including at the currently recommended frequency of STI testing once every three months for individuals on PrEP. Moreover, the model predicts that a higher STI testing frequency alone is not enough to prevent a rise in gonorrhea prevalence, unless the testing frequency is increased to impractical levels. However, testing every 2 months in combination with a 10–25 % reduction in risky behavior by individuals on PrEP would maintain gonorrhea prevalence at pre-PrEP levels. The results emphasize that programs making PrEP more available should be accompanied by efforts to support condom usage and frequent STI testing, in order to avoid an increase in the prevalence of gonorrhea and other bacterial STIs.

Yourdkhani, Samaneh; Rhodes, John A.

doi: 10.1007/s11538-020-00773-4pmid: 32676801

A metric phylogenetic tree relating a collection of taxa induces weighted rooted triples and weighted quartets for all subsets of three and four taxa, respectively. New intertaxon distances are defined that can be calculated from these weights, and shown to exactly fit the same tree topology, but with edge weights rescaled by certain factors dependent on the associated split size. These distances are analogs for metric trees of similar ones recently introduced for topological trees that are based on induced unweighted rooted triples and quartets. The distances introduced here lead to new statistically consistent methods of inferring a metric species tree from a collection of topological gene trees generated under the multispecies coalescent model of incomplete lineage sorting. Simulations provide insight into their potential.

Samson, Julia E.; Ray, Dylan D.; Porfiri, Maurizio; Miller, Laura A.; Garnier, Simon

doi: 10.1007/s11538-020-00759-2pmid: 32638174

Xeniid corals (Cnidaria: Alcyonacea), a family of soft corals, include species displaying a characteristic pulsing behavior. This behavior has been shown to increase oxygen diffusion away from the coral tissue, resulting in higher photosynthetic rates from mutualistic symbionts. Maintaining such a pulsing behavior comes at a high energetic cost, and it has been proposed that coordinating the pulse of individual polyps within a colony might enhance the efficiency of fluid transport. In this paper, we test whether patterns of collective pulsing emerge in coral colonies and investigate possible interactions between polyps within a colony. We video recorded different colonies of Heteroxenia sp. in a laboratory environment. Our methodology is based on the systematic integration of a computer vision algorithm (ISOMAP) and an information-theoretic approach (transfer entropy), offering a vantage point to assess coordination in collective pulsing. Perhaps surprisingly, we did not detect any form of collective pulsing behavior in the colonies. Using artificial data sets, however, we do demonstrate that our methodology is capable of detecting even weak information transfer. The lack of a coordination is consistent with previous work on many cnidarians where coordination between actively pulsing polyps and medusa has not been observed. In our companion paper, we show that there is no fluid dynamic benefit of coordinated pulsing, supporting this result. The lack of coordination coupled with no obvious fluid dynamic benefit to grouping suggests that there may be non-fluid mechanical advantages to forming colonies, such as predator avoidance and defense.

Fatoyinbo, H. O.; Brown, R. G.; Simpson, D. J. W.; van Brunt, B.

doi: 10.1007/s11538-020-00771-6pmid: 32676881

Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as pacemaker dynamics. In this article, we address pacemaker dynamics associated with the interaction of Ca2+\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text {Ca}}^{2+}$$\end{document} and K+\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\text {K}^+$$\end{document} fluxes in the cell membrane of a smooth muscle cell. First we reduce a pacemaker model to a two-dimensional system equivalent to the reduced Morris–Lecar model and then perform a detailed numerical bifurcation analysis of the reduced model. Existing bifurcation analyses of the Morris–Lecar model concentrate on external applied current, whereas we focus on parameters that model the response of the cell to changes in transmural pressure. We reveal a transition between Type I and Type II excitabilities with no external current required. We also compute a two-parameter bifurcation diagram and show how the transition is explained by the bifurcation structure.

Sooknanan, J.; Comissiong, D. M. G.

doi: 10.1007/s11538-020-00757-4pmid: 32617673

Social media plays an important role in alerting and educating the public during disease outbreaks. By increasing awareness of the disease and its prevention, it can lead to a modification of behaviour which then affects contact/incidence rates. Social media data may also be used when formulating, developing and parameterising models. As mobile technology continues to evolve and proliferate, social media is expected to occupy an increasingly prominent role in the field of infectious disease modelling to improve their predictive power. This article presents a review of existing models incorporating media in general and highlights opportunities for social media to enhance traditional compartmental models so as to make the best use of this resource in controlling the spread of disease.

Cozzens, Margaret; Roberts, Fred S.

doi: 10.1007/s11538-020-00761-8pmid: 32638175

This paper focuses on issues concerning the introductory college mathematics sequence with an emphasis on students interested in the life sciences, and concentration on the time after the publication of BIO2010 (BIO2010 in Transforming Undergraduate Education for Future Research Biologists, National Academies of Science, Medicine and Engineering, Washington, 2003). It also explores the potential uses of books targeted at introductory mathematics courses for life science majors today. As relevant background, we look at the evolution of the way that calculus has been taught over the past 50 years, including at the high school level. We also explore the implications of changes in technology and course delivery, such as online education. As we discuss different books and introductory course ideas, we focus on the needs of biology students, the inclusion of real-world problems and models, the role of technology, and the impact of data science. The paper is organized as follows: Sect. 1 provides some personal background with calculus dating back to the 1970s, and changes in calculus prior to BIO2010. Section 2 introduces goals for an introductory mathematics sequence and evaluates the calculus sequence in light of those goals. Sections 3–7 discuss various issues that will help to understand issues and challenges for introductory mathematics for the life sciences: Calculus in high school (Sect. 3), equity issues relative to calculus and other math topics (Sect. 4), the impact of online education (Sect. 5), math as a stumbling block for college students (Sect. 6), and the increasing importance and value of teaching data science (Sect. 7). Section 8 reviews the development of books in light of these issues and challenges. The last section (Sect. 9) summarizes conclusions.

Hiller, Rebecca M.; von Kügelgen, Julius; Bao, Huan; Duong Van Hoa, Franck; Cytrynbaum, Eric N.

doi: 10.1007/s11538-020-00772-5pmid: 32653954

The original version of this article unfortunately contained a mistake. The co-author Dr. Franck Duong Van Hoa first name and last name were misinterpreted in the original publication.