Analysis of SIR Mathematical Model for Malaria Disease: A Study in Assam, India

The global outbreak of covid-19 pandemic is still affecting people around the globe very badly. Before the covid-19 pandemic outbreak, several research works were done for the detection and prevention of various infectious diseases using different mathematical modeling. Implementing mathematical modeling to resolve problems in Biology and physiology is generally called Mathematical Biology, an extremely interdisciplinary area. The applications of mathematical modeling in the analysis of infectious diseases help to concentrate on the necessary processes associated with forming the infectious disease epidemiology and specifications estimation. The compartmental mathematical model can be either SI, SIS, SIR, SIRS, or SEIR where S, I, R, and E denote susceptible, infected, recovered, and exposed respectively. Malaria is an infectious disease that has a large economic and health impact on society. This study aims to predict the estimation of suspected, infected and recovered people using the SIR mathematical model of the Barama area of Baksa District in Assam, India. Here we analyzed the Basic Reproductive Ratio of the SIR model for malaria disease and examined if malaria is epidemic or endemic in that area

Game and decision theory in mathematics education: epistemological, cognitive and didactical perspectives

In the 1950s, game and decision theoretic modeling emerged—based on applications in the social sciences—both as a domain of mathematics and interdisciplinary fields. Mathematics educators, such as Hans Georg Steiner, utilized game theoretical modeling to demonstrate processes of mathematization of real world situations that required only elementary intuitive understanding of sets and operations. When dealing with n-person games or voting bodies, even students of the 11th and 12th grade became involved in what Steiner called the evolution of mathematics from situations, building of mathematical models of given realities, mathematization, local organization and axiomatization. Thus, the students could participate in processes of epistemological evolutions in the small scale. This paper introduces and discusses the epistemological, cognitive and didactical aspects of the process and the roles these activities can play in the learning and understanding of mathematics and mathematical modeling. It is suggested that a project oriented study of game and decision theory can develop situational literacy, which can be of interest for both mathematics education and general educatio

Eco-evolutionary dynamics with environmental feedback: cooperation in a changing world

Eco-evolutionary game dynamics which characterizes the mutual interactions and the coupled evolutions of strategies and environments has been of growing interests in very recent years. Since such feedback loops widely exist in a range of coevolutionary systems, such as microbial systems, social-ecological system and psychological-economic system, recent modeling frameworks that unveil the oscillating dynamics of social dilemmas have great potential for practical applications. In this perspective article, we overview the latest progress of evolutionary game theory in this direction. We describe both mathematical methods and interdisciplinary applications across different fields. The ideas worthy of further consideration are discussed in prospects, with the central role of promoting cooperations in a changing world

Deterministic Dynamics and Chaos: Epistemology and Interdisciplinary Methodology

We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary relation between mathematics and psychology, focused on the mathematical theory of deterministic dynamical systems, and in particular, on the theory of chaos. On one hand, there is the direct classic relation: the application of mathematics to psychology. On the other hand, we propose the converse relation which consists in the formulation of new abstract mathematical problems appearing from processes and structures under research of psychology. The bidirectional multidisciplinary relation from-to pure mathematics, largely holds with the "hard" sciences, typically physics and astronomy. But it is rather new, from the social and human sciences, towards pure mathematics

Mathematical and Computational Applications in Disease and Landscape Ecology

The Individualized Interdisciplinary Program (IIP) at the University of Montana allows students to work with faculty in the design of a graduate curriculum tailored to their unique academic, creative, and professional needs. The principal goal of the National Science Foundation\u27s IGERT: Montana - Ecology of Infectious Diseases (MEID) program is to produce graduates with expertise to lead the collaborative, cross-, and inter-disciplinary efforts in education and research needed to address complex problems as exemplified by the ecology of endemic, epidemic, and emergent infectious diseases. Under the envelope of these two programs, I have developed a Ph.D. program in which I received an interdisciplinary education in applied mathematics and computational ecology. I strongly feel that spatial modeling is one of the most promising approaches to advance the sciences of disease ecology and landscape ecology. Mathematical and computational modeling provide powerful tools for evaluating relationships between mechanisms and responses in a spatially complex environment. Past progress in these fields has been limited by the lack of computational power and flexible mathematical models to simulate the actions of ecosystem and population processes in complex environments. My specific research focus is in the development of mathematical and computational models to synthesize environmental data for describing and predicting the characteristics of population and disease dynamics on the landscape. The results from this research are documented in the following chapters: 1) Mathematical Disease Ecology. This uses numerical and qualitative analysis to study a model for Tick Borne Relapsing Fever in an island ecosystem. 2) Computational Landscape Ecology. The development and applications of a spatially-explicit computer model to predict population connectivity and geneflow on complex landscapes are described

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie

Virginia Commonwealth University\u27s Program for K-6 and 6-8 Teachers: The Interdisciplinary B.S. in Science

Virginia Commonwealth University (VCU) has very recently revised its requirements for the K-6 Certification to include a total of 21 hours in mathematics and science as well as a three credit hour methods course in mathematics and science. This requirement includes a physical science and a biological science course, each with a laboratory component, a contemporary mathematics course with extensive student projects, collaborative work and applications, a statistics course and interdisciplinary science and mathematics course. We believe that as students complete these requirements they will meet the new State K-6 licensure requirements in all areas, with the exception of geometry. We are developing a new geometry course that we hope will be required of all future teachers. The challenge of preparing middle school teachers to teach mathematics and/or science is much more difficult. VCU has been preparing very few middle school teachers of mathematics and science. We typically averaged less than one middle school science teacher and less than one middle school mathematics teacher per year. This paper provides a description of our interdisciplinary degree in mathematics and science that appears to be attracting significant numbers of students with an interest in teaching mathematics and/or science at the middle school level

NEXUS/Physics: An interdisciplinary repurposing of physics for biologists

In response to increasing calls for the reform of the undergraduate science curriculum for life science majors and pre-medical students (Bio2010, Scientific Foundations for Future Physicians, Vision & Change), an interdisciplinary team has created NEXUS/Physics: a repurposing of an introductory physics curriculum for the life sciences. The curriculum interacts strongly and supportively with introductory biology and chemistry courses taken by life sciences students, with the goal of helping students build general, multi-discipline scientific competencies. In order to do this, our two-semester NEXUS/Physics course sequence is positioned as a second year course so students will have had some exposure to basic concepts in biology and chemistry. NEXUS/Physics stresses interdisciplinary examples and the content differs markedly from traditional introductory physics to facilitate this. It extends the discussion of energy to include interatomic potentials and chemical reactions, the discussion of thermodynamics to include enthalpy and Gibbs free energy, and includes a serious discussion of random vs. coherent motion including diffusion. The development of instructional materials is coordinated with careful education research. Both the new content and the results of the research are described in a series of papers for which this paper serves as an overview and context.Comment: 12 page