Finite dimensional state representation of physiologically structured populations

In a physiologically structured population model (PSPM) individuals are characterised by continuous variables, like age and size, collectively called their i-state. The world in which these individuals live is characterised by another set of variables, collectively called the environmental condition. The model consists of submodels for (i) the dynamics of the i-state, e.g. growth and maturation, (ii) survival, (iii) reproduction, with the relevant rates described as a function of (i-state, environmental condition), (iv) functions of (i-state, environmental condition), like biomass or feeding rate, that integrated over the i-state distribution together produce the output of the population model. When the environmental condition is treated as a given function of time (input), the population model becomes linear in the state. Density dependence and interaction with other populations is captured by feedback via a shared environment, i.e., by letting the environmental condition be influenced by the populations' outputs. This yields a systematic methodology for formulating community models by coupling nonlinear input-output relations defined by state-linear population models. For some combinations of submodels an (infinite dimensional) PSPM can without loss of relevant information be replaced by a finite dimensional ODE. We then call the model ODE-reducible. The present paper provides (a) a test for checking whether a PSPM is ODE reducible, and (b) a catalogue of all possible ODE-reducible models given certain restrictions, to wit: (i) the i-state dynamics is deterministic, (ii) the i-state space is one-dimensional, (iii) the birth rate can be written as a finite sum of environment-dependent distributions over the birth states weighted by environment independent 'population outputs'. So under these restrictions our conditions for ODE-reducibility are not only sufficient but in fact necessary. Restriction (iii) has the desirable effect that it guarantees that the population trajectories are after a while fully determined by the solution of the ODE so that the latter gives a complete picture of the dynamics of the population and not just of its outputs.Peer reviewe

On models of physiologically structured populations and their reduction to ordinary differential equations

Considering the environmental condition as a given function of time, we formulate a physiologically structured population model as a linear non-autonomous integral equation for the, in general distributed, population level birth rate. We take this renewal equation as the starting point for addressing the following question: When does a physiologically structured population model allow reduction to an ODE without loss of relevant information? We formulate a precise condition for models in which the state of individuals changes deterministically, that is, according to an ODE. Specialising to a one-dimensional individual state, like size, we present various sufficient conditions in terms of individual growth-, death-, and reproduction rates, giving special attention to cell fission into two equal parts and to the catalogue derived in an other paper of ours (submitted). We also show how to derive an ODE system describing the asymptotic large time behaviour of the population when growth, death and reproduction all depend on the environmental condition through a common factor (so for a very strict form of physiological age).Peer reviewe

Finite dimensional state representation of physiologically structured populations (vol 80, pg 205, 2020)

Correction to Journal of Mathematical Biology (2020) 80:205–273 https://doi.org/10.1007/s00285-019-01454-0In the original publication of the article, the Subsection 2.1.2 was published incorrectly.Peer reviewe

Exploring the ethical dilemmas of afro-centric social media use through agent-based modeling: A review

Social media (SM) has become indispensable for individuals and workplaces/organizations in Africa and beyond. Therein, ethical concerns are posed due to the inability to create virtual boundaries (VM), the intractability of guidelines for managers and other unintended risks/con­sequences. Operations research was used for modeling ethical concerns but have been defeated due to reasons of several ethical values and various assessment criteria for stakeholders. Conse­quently, this review paper initially x-rays the import of ethical dilemmas in older studies so as to conceive a strategy characterized by engaging stakeholders that utilize SM via Agent-Based Modeling (ABM), in such a manner that ethics can be evaluated. Additionally, it presented the rudiments of social media ABM explorations and the peculiarities of Africa. Finally, the review provided a suitable methodology and sheds light on the possible challenges of ABM implementation. Besides the benefit of increased patronage, the agent technology may also constitute a pedagogical tool for learning ethical behavior. Moreover, it is our hope that with the involvement of experts of related disciplines in Africa, attendant theories are formalized and used for building agent models that allows ethical decision making, weighing of pros and cons, analyzing differences and dimensions inherent in VM creation

Histopathological effects of Cyperdicot and vitamin E supplementation on selected organs of Clarias gariepinus (Burchell, 1822) reared in a tropical fish farm in Nigeria

This study conducted in 2014 investigated the histopathological effects of Cyperdicot and vitamin E supplementation on some selected organs in juveniles of Clarias gariepinus. Fish were exposed to 0. 0.08 and 0.16 mg/L Cyperdicot and vitamin E. Fish were divided into six groups: control, 0.80 mg/L; Cyperdicot, 0.16 mg/L; Cyperdicot, vitamin E, vitamin E + 0.08 mg/L Cyperdicot, and vitamin E + 0.16 m/L Cyperdicot insecticide. There was significant relation between temperature, pH, and dissolved oxygen with Cyperdicot concentration. The LC50 value based on probit analysis was found to be 0.08 mg/L for 96 h. Samples were taken at fixed times for histopathological studies. The fish exhibited behavioural and dermatological changes. Vitamin E + 0.08 mg/L Cyperdicot and vitamin E + 0.16 mg/L Cyperdicot treated fish showed abnormalities in their behaviour. Gills, liver, and kidneys of the 0.08 mg/L Cyperdicot treated group also showed several histopathological changes during the experimental periods. The organs of the fish treated with vitamin E + 0.16 mg/L Cyperdicot induced histopathological changes. The toxic effect of Cyperdicot is clear on the behavioural and histopathological aspects of the fish gills, liver, and kidney tissues, while vitamin E had no amelioration effects on them.Keywords: Cyperdicot, vitamin E, Clarias gariepinus, pesticide, sub lethal toxicit

Characterizing the Initial Phase of Epidemic Growth on some Empirical Networks

A key parameter in models for the spread of infectious diseases is the basic reproduction number $R_0$, which is the expected number of secondary cases a typical infected primary case infects during its infectious period in a large mostly susceptible population. In order for this quantity to be meaningful, the initial expected growth of the number of infectious individuals in the large-population limit should be exponential. We investigate to what extent this assumption is valid by performing repeated simulations of epidemics on selected empirical networks, viewing each epidemic as a random process in discrete time. The initial phase of each epidemic is analyzed by fitting the number of infected people at each time step to a generalised growth model, allowing for estimating the shape of the growth. For reference, similar investigations are done on some elementary graphs such as integer lattices in different dimensions and configuration model graphs, for which the early epidemic behaviour is known. We find that for the empirical networks tested in this paper, exponential growth characterizes the early stages of the epidemic, except when the network is restricted by a strong low-dimensional spacial constraint, such as is the case for the two-dimensional square lattice. However, on finite integer lattices of sufficiently high dimension, the early development of epidemics shows exponential growth.Comment: To be included in the conference proceedings for SPAS 2017 (International Conference on Stochastic Processes and Algebraic Structures), October 4-6, 201

Knowledge, perception and willingness to receive the current COVID-19 vaccine among residents of Awka metropolis, Anambra State, Nigeria

Background: Vaccines can effectively reduce most morbidities and mortalities caused by infectious agents. The emergence of the COVID-19 vaccine may be accompanied with huge success in containing the pandemic. The aim of the study was to assesses knowledge, perception and willingness to receive the current COVID-19 vaccine among residents in Awka metropolis, Anambra State, Nigeria.Methods: Using a pre-tested semi-structured questionnaire, this study was conducted in Awka metropolis Anambra State, Nigeria among 393 respondents (aged 18 years and above), and analyzed to assess their knowledge, perception and willingness to receive the current COVID-19 vaccine. Statistical package for social sciences software (SPSS) version 23.0 was used, descriptive statistics were reported in frequencies and percentages, Chi-square test was used to assess the association between socio-demographic characteristics and willingness to receive the vaccine, and level of significance was set at p<0.05.Results: The results showed that all respondents (100%) have good knowledge of the vaccine availability. Only 25.7% were willing to receive the vaccine, although 57.3% were willing to receive any other vaccine apart from the COVID-19 vaccine. Very few respondents (18.3%) thinks the vaccine is accessible to all. Most of the respondents (72%) did not support mandatory implementation of COVID-19 vaccine in Nigeria. Among the socio-demographic characteristics, only occupation was significantly associated with willingness to receive the vaccine (p=0.010, χ2=20.214).  Conclusions: This study highlighted the need to effectively educate the masses through appropriate public health literacy programs and enlightenment campaigns on the role of the vaccine in curbing this pandemic

Thermal Conversion of Guanylurea Dicyanamide into Graphitic Carbon Nitride via Prototype CNx Precursors

Guanylurea dicyanamide, [(H2N)C(-O)NHC(NH2)2][N(CN)2], has been synthesized by ion exchange reaction in aqueous solution and structurally characterized by single-crystal X-ray diffraction (C2/c, a = 2249.0(5) pm, b = 483.9(1) pm, c = 1382.4(3) pm, β = 99.49(3)°, V = 1483.8(5) × 106 pm3, T = 130 K). The thermal behavior of the molecular salt has been studied by thermal analysis, temperature-programmed X-ray powder diffraction, FTIR spectroscopy, and mass spectrometry between room temperature and 823 K. The results were interpreted on a molecular level in terms of a sequence of thermally induced addition, cyclization, and elimination reactions. As a consequence, melamine (2,4,6-triamino-1,3,5-triazine) is formed with concomitant loss of HNCO. Further condensation of melamine yields the prototypic CNx precursor melem (2,6,10-triamino-s-heptazine, C6N7(NH2)3), which alongside varying amounts of directly formed CNxHy material transforms into layered CNxHy phases without significant integration of oxygen into the core framework owing to the evaporation of HNCO. Thus, further evidence can be added to melamine and its condensation product melem acting as “key intermediates” in the synthetic pathway toward graphitic CNxHy materials, whose exact constitution is still a point at issue. Due to the characteristic formation process and hydrogen content a close relationship with the polymer melon is evident. In particular, the thermal transformation of guanylurea dicyanamide clearly demonstrates that the formation of volatile compounds such as HNCO during thermal decomposition may render a large variety of previously not considered molecular compounds suitable CNx precursors despite the presence of oxygen in the starting material

Ascertaining the Overall Occurrence of Dental Fluorosis in Students of Selected Secondary Schools in Rivers State

Public health places a premium on understanding the amount of fluoride in potable water and other toothpastes, as well as how it affects skeletal and dental tissues to cause fluorosis. Fluorosis is, however, poorly understood and known in Nigeria. The goal of this research was to Ascertain the Overall Occurrence of Dental Fluorosis in Students of Selected Secondary Schools in Rivers State. A cross-sectional survey of 541 students from selected secondary schools in Rivers State who were between the ages of 9 and 17 was carried out. All students present at school on the day of data collection had their mouths examined by oral health professionals as part of a quasi-experimental method. Each subject was supported by a torch light while seated on a chair, and their teeth were examined for dental fluorosis in their wet state. The presence of dental fluorosis and the severity of it were documented using Dean's Dental Fluorosis. The presence of dental fluorosis and the severity of it were documented using Dean's Dental Fluorosis. (358) Dental fluorosis impacted 66.17% of the students, varying in severity from very mild to severe cases