Stability Analysis of a Mathematical Model for Onchocerciaisis Disease Dynamics

In this work, we propose a Deterministic Mathematical Model that Combines Infectious but not Blind and Infectious Blind Compartments for Onchocerciasis Transmission and Control. Onchocerciasis is usually the term used to describe river blindness, it is a disease that causes blindness, and the second largest cause of blindness after trachoma. It mainly affects the eyes and the skin. The equilibrium states of the model are obtained. The disease free equilibrium state is analysed for stability; the condition for its stability is obtained as an inequality constraint on the parameters. Results shows that although, a 60% treatment coverage rate of infected and infectious blind individuals only is better than 80% treatment coverage rate of infected but not blind individuals only. Also, all the four control strategies reduce the effective reproduction number below unity. A 40% coverage rate of fumigation and treatment of infectious but not blind is better than a 40%coverage rate of fumigation only. It further reveals that a 30% coverage rate of fumigation and treatment of infectious blind is better than 80%coverage rate of fumigation only or fumigation and treatment of infected but not blind only. We are able to show that disease free equilibrium and endemic equilibrium exists and are both locally and globally stable, and we computed the Rc of the model and showed that it is a parameter to test for stability, we also use the Jacobi stability technique to show that disease free equilibrium and endemic equilibrium are both locally and globally stable. The sensitivity analysis results shows that the most sensitive parameter is ρ while the least sensitive is  μvKeywords: Onchocerciasis, Mathematical model, Equilibrium state, Deterministic, Effective reproductive number, Stability

Mathematical Modeling of Biological Systems

Mathematical modeling is a powerful approach supporting the investigation of open problems in natural sciences, in particular physics, biology and medicine. Applied mathematics allows to translate the available information about real-world phenomena into mathematical objects and concepts. Mathematical models are useful descriptive tools that allow to gather the salient aspects of complex biological systems along with their fundamental governing laws, by elucidating the system behavior in time and space, also evidencing symmetry, or symmetry breaking, in geometry and morphology. Additionally, mathematical models are useful predictive tools able to reliably forecast the future system evolution or its response to specific inputs. More importantly, concerning biomedical systems, such models can even become prescriptive tools, allowing effective, sometimes optimal, intervention strategies for the treatment and control of pathological states to be planned. The application of mathematical physics, nonlinear analysis, systems and control theory to the study of biological and medical systems results in the formulation of new challenging problems for the scientific community. This Special Issue includes innovative contributions of experienced researchers in the field of mathematical modelling applied to biology and medicine

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative

Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a mathematical equation for prediction. In this work, a model of the well-known river blindness disease is created via the Caputo and beta derivatives. A partial study of stability analysis was presented. The extended system describing the spread of this disease was solved via two analytical techniques: the Laplace perturbation and the homotopy decomposition methods. Summaries of the iteration methods used were provided to derive special solutions to the extended systems. Employing some theoretical parameters, we present some numerical simulations

Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative

Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a mathematical equation for prediction. In this work, a model of the well-known river blindness disease is created via the Caputo and beta derivatives. A partial study of stability analysis was presented. The extended system describing the spread of this disease was solved via two analytical techniques: the Laplace perturbation and the homotopy decomposition methods. Summaries of the iteration methods used were provided to derive special solutions to the extended systems. Employing some theoretical parameters, we present some numerical simulations

Environmental Effects of Stratospheric Ozone Depletion, UV Radiation, and interactions with Climate Change: 2022 Assessment Report

The Montreal Protocol on Substances that Deplete the Ozone Layer was established 35 years ago following the 1985 Vienna Convention for protection of the environment and human health against excessive amounts of harmful ultraviolet-B (UV-B, 280-315 nm) radiation reaching the Earth’s surface due to a reduced UV-B-absorbing ozone layer. The Montreal Protocol, ratified globally by all 198 Parties (countries), controls ca 100 ozone-depleting substances (ODS). These substances have been used in many applications, such as in refrigerants, air conditioners, aerosol propellants, fumigants against pests, fire extinguishers, and foam materials. The Montreal Protocol has phased out nearly 99% of ODS, including ODS with high global warming potentials such as chlorofluorocarbons (CFC), thus serving a dual purpose. However, some of the replacements for ODS also have high global warming potentials, for example, the hydrofluorocarbons (HFCs). Several of these replacements have been added to the substances controlled by the Montreal Protocol. The HFCs are now being phased down under the Kigali Amendment. As of December 2022, 145 countries have signed the Kigali Amendment, exemplifying key additional outcomes of the Montreal Protocol, namely, that of also curbing climate warming and stimulating innovations to increase energy efficiency of cooling equipment used industrially as well as domestically. As the concentrations of ODS decline in the upper atmosphere, the stratospheric ozone layer is projected to recover to pre-1980 levels by the middle of the 21st century, assuming full compliance with the control measures of the Montreal Protocol. However, in the coming decades, the ozone layer will be increasingly influenced by emissions of greenhouse gases and ensuing global warming. These trends are highly likely to modify the amount of UV radiation reaching the Earth\u27s surface with implications for the effects on ecosystems and human health. Against this background, four Panels of experts were established in 1988 to support and advise the Parties to the Montreal Protocol with up-to-date information to facilitate decisions for protecting the stratospheric ozone layer. In 1990 the four Panels were consolidated into three, the Scientific Assessment Panel, the Environmental Effects Assessment Panel, and the Technology and Economic Assessment Panel. Every four years, each of the Panels provides their Quadrennial Assessments as well as a Synthesis Report that summarises the key findings of all the Panels. In the in-between years leading up to the quadrennial, the Panels continue to inform the Parties to the Montreal Protocol of new scientific information

ABC Transporters in Human Diseases

Mammalian ATP-binding cassette (ABC) transporters constitute a superfamily of proteins involved in many essential cellular processes. Most of these transporters are transmembrane proteins and allow the active transport of solutes, small molecules, and lipids across biological membranes. On the one hand, some of these transporters are involved in drug resistance (also referred to as MDR or multidrug resistance), a process known to be a major brake in most anticancer treatments, and the medical challenge is thus to specifically inhibit their function. On the other hand, molecular defects in some of these ABC transporters are correlated with several rare human diseases, the most well-documented of which being cystic fibrosis, which is caused by genetic variations in ABCC7/CFTR (cystic fibrosis transmembrane conductance regulator). In the latter case, the goal is to rescue the function of the deficient transporters using various means, such as targeted pharmacotherapies and cell or gene therapy. The aim of this Special Issue, “ABC Transporters in Human Diseases”, is to present, through original articles and reviews, the state-of-the-art of our current knowledge about the role of ABC transporters in human diseases and the proposed therapeutic options based on studies ranging from cell and animal models to patients