Relationship between blood superoxide dismutase activity and zinc, copper, glutathione and metallothioneines concentrations in calves

RedOx processes determine the resistance of the organism to pollutants. The aim of the study was to establish a possible relationship between copper and zinc concentration in the blood of calves and the enzyme activity of superoxide dismutase. The study was conducted in 2019 on 50 calves with a weight of 201-250 kg. The samples of venous blood were taken to estimate the level of hemoglobin, glutathione, metallothioneins, as well as zinc, copper, and superoxide dismutase activity. The obtained average values of these substances concentration were compared between each other. A positive correlation between the activity of superoxide dismutase and the concentration of zinc (r = 0.64) and copper (r = 0.87) in the blood of calves has been established. It may be because both metals are obligatory components of superoxide dismutase. There is also a positive relationship between the levels of copper and zinc (r = 0.68). For the other parameters, no reliable relationship was found. The data obtained indicate a positive relationship between the activity of superoxide dismutase and metal concentrations of copper and zinc in the blood of calves. At the same time, a more significant positive relationship is established for copper.

Age-structured delayed SIPCV epidemic model of HPV and cervical cancer cells dynamics I. Numerical method

The numerical method for simulation dynamics of nonlinear epidemic model of age-structured sub-populations of susceptible, infectious, precancerous and cancer cells and unstructured population of human papilloma virus (HPV) is developed (SIPCV model). Cell population dynamics is described by the initial-boundary value problem for the delayed semi-linear hyperbolic equations with age- and time-dependent coefficients and HPV dynamics is described by the initial problem for nonlinear delayed ODE. The model considers two time-delay parameters: the time between viral entry into a target susceptible cell and the production of new virus particles, and duration of the first stage of delayed immune response to HPV population growing. Using the method of characteristics and method of steps we obtain the exact solution of the SIPCV epidemic model in the form of explicit recurrent formulae. The numerical method designed for this solution and used the trapezoidal rule for integrals in recurrent formulae has a second order of accuracy. Numerical experiments with vanished mesh spacing illustrate the second order of accuracy of numerical solution with respect to the benchmark solution and show the dynamical regimes of cell-HPV population with the different phase portraits.

Some mathematical tools for modelling malaria: a subjective survey

In this paper, we provide a brief survey of mathematical modelling of malaria and how it is used to understand the transmission and progression of the disease and design strategies for its control to support public health interventions and decision-making. We discuss some of the past and present contributions of mathematical modelling of malaria, including the recent development of modelling the transmission-blocking drugs. We also comment on the complexity of the malaria dynamics and, in particular, on its multiscale character with its challenges and opportunities. We illustrate the discussion by presenting a curve fitting using a 95% confidence interval for the South African data for malaria from the years 2001-2018$ and provide projections for the number of malaria cases and deaths up to the year 2025.

The Gompertz model revisited and modified using reaction networks: Mathematical analysis

In the present work we discuss the?usage of the framework of chemical reaction networks for the construction of dynamical models and their mathematical analysis. To this end, the process of construction of reaction-network-based models via mass action kinetics is introduced and illustrated on several familiar examples,?such as the exponential (radioactive) decay, the logistic and the Gompertz models. Our final goal is to modify the reaction network of the classic Gompertz model in a natural way using certain features of the exponential decay and the logistic models. The growth function of the obtained new Gompertz-type hybrid model possesses an additional degree of freedom (one more rate parameter) and is thus more flexible when applied to numerical simulation of measurement and experimental data sets. More specifically, the ordinate (height) of the inflection point of the new generalized Gompertz model can vary in the interval (0, 1/e], whereas the respective height of the classic Gompertz model is fixed at 1/e (assuming the height of the upper asymptote is one). It is shown that?the new model is a generalization of both the classic Gompertz model and the one-step exponential decay model.?Historically the Gompertz function has been first used for statistical/insurance purposes, much later this function has been applied to simulate biological growth data sets coming from various fields of science, the reaction network approach explains and unifies the two approaches.

Qualitative analysis of a mathematical model about population of green turtles on the Galapagos island

According to the IUCN, most sea turtles fall into one of the endangered categories. Since, sea turtles, like many other reptiles, present an unusual developmental process, marked by the determination of the sex of the offspring by environmental factors, more specifically by temperature. In the temperature sex determination (TSD) system the temperature of an embryo's environment during incubation period will dictate the embryo's sex development. This developmental process, together with the complex mating and nesting behavior and the vulnerability of sea turtles to threats of a natural or anthropogenic nature, naturally lead to the study of the population dynamics of the species.? For this reason, in this paper, we have developed a continuous model given by a system of three ordinary differential equations to study the dynamics of the green sea turtle population long-term, focusing the mathematical simulations on the data obtained for the nesting species of Galapagos Islands. Through the qualitative analysis of the model, the following is demonstrated: 1) The flow induced by the system is positively invariant on the region of biological interest and 2). The given condition on is necessary and sufficient for the unique nontrivial equilibrium point to be globally asymptotically stable in that region. When implementing the estimated values for our parameters in the numerical simulations, it was observed that indeed the population of Galapagos green sea turtles complies with the condition for which the nontrivial critical point is globally asymptotically stable.

Mathematical model for acquiring immunity to malaria: a PDE approach

We develop a new model of integro-differential equations coupled with a partial differential equation that focuses on the study of the? naturally acquiring immunity to malaria induced by exposure to infection. We analyze a continuous acquisition of immunity after infected individuals are treated. It exhibits complex and realistic mechanisms precised mathematically in both disease free or endemic context and in several numerical simulations showing the interplay between infection through the bite of mosquitoes. The model confirms the (partial) premunition of the human population in the regions where malaria is endemic. As common in literature, we indicate an equivalence of the basic reproduction rate as the spectral radius of a next generation operator.

Mathematical Modeling and Analysis of Covid-19 Infection spreads in India with Restricted Optimal Treatment on Disease Incidence

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

COVID-19 changing the face of the world. Can sub-Sahara Africa cope?

We formulate a mathematical model for the spread of the coronavirus which incorporates adherence to disease prevention. The major results of this study are: first, we determined optimal infection coefficients such that high levels of coronavirus transmission are prevented. Secondly, we have found that there? exists several optimal pairs of removal rates, from the general population of asymptomatic and symptomatic infectives respectively that can protect hospital bed capacity and flatten the hospital admission curve. Of the many optimal strategies, this study recommends the pair that yields the least number of coronavirus related deaths. The results for South Africa, which is better placed than the other sub-Sahara African countries, show that failure to address hygiene and adherence issues will preclude the existence of an optimal strategy and could result in a more severe epidemic than the Italian COVID-19 epidemic. Relaxing lockdown measures to allow individuals to attend to vital needs such as food replenishment increases household and community infection rates and the severity of the overall infection.

Scenarios for the spread of COVID-19 analyzed by the TVBG-SEIR spline model

We develop a novel TVBG-SEIR spline model for analysis of the coronavirus infection (COVID-19). It aims to analyze the long-term global evolution of the epidemics "controlled" by the introduction of lockdown/open up measures by the authorities. The incorporation of different "lockdown scenarios" varying in time permits to analyze not only the primary epidemic wave but also the arising secondary wave and any further waves.The model is supplied by a web-based Scenario Building Tool for COVID-19 (called shortly SBT-COVID19) which may be used as a decision support software by (health) policy makers to explore various scenarios. This can be achieved by controlling/changing the scale of the containment measures (home and social isolation/quarantine, travel restrictions and other) and to assess their effectiveness. In particular, the SBT-COVID19 Tool permits to assess how long the lockdown measures should be maintained.

Scenarios for the spread of COVID-19 analyzed by the TVBG-SEIR spline model

We develop a novel TVBG-SEIR spline model for analysis of the coronavirus infection (COVID-19). It aims to analyze the long-term global evolution of the epidemics "controlled" by the introduction of lockdown/open up measures by the authorities. The incorporation of different "lockdown scenarios" varying in time permits to analyze not only the primary epidemic wave but also the arising secondary wave and any further waves.The model is supplied by a web-based Scenario Building Tool for COVID-19 (called shortly SBT-COVID19) which may be used as a decision support software by (health) policy makers to explore various scenarios. This can be achieved by controlling/changing the scale of the containment measures (home and social isolation/quarantine, travel restrictions and other) and to assess their effectiveness. In particular, the SBT-COVID19 Tool permits to assess how long the lockdown measures should be maintained.