Mathematical Modeling for Society and Biology second edition draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For the new edition, the author uses mathematical models tat are simple, transparent, and verifiable. Also new to the book is an introduction to mathematical concepts that every quantitative scientist in the biological and social sciences should be familiar with, such as Bayesian inference and differential equations. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced -- P. 4 of cover
For more than a year, the COVID-19 pandemic has been a major public health issue, affecting the lives of most people around the world. With both people's health and the economy at great risks, governments rushed to control the spread of the virus. Containment measures were heavily enforced worldwide until a vaccine was developed and distributed. Although researchers today know more about the characteristics of the virus, a lot of work still needs to be done in order to completely remove the disease from the population. However, this is true for most of the infectious diseases in existence, including Influenza, Dengue fever, Ebola, Malaria, and Zika virus. Understanding the transmission process of a disease is usually acquired through biological and chemical studies. In addition, mathematical models and computational simulations offer different approaches to predict the number of infectious cases and identify the transmission patterns of a disease. Information obtained helps provide effective vaccination interventions, quarantine and isolation strategies, and treatment plans to reduce disease transmissions and prevent potential outbreaks. The focus of this paper is to investigate the spread of COVID-19 and its effect on a population through mathematical models. Specifically, we use SEIR and SEIR with vaccine models to formulate the spread of COVID-19, where S, E, I, R, and V are susceptible, exposed, infected, recovered, and vaccinated compartments, respectively. With these two models we calculate a central quantity in epidemiology called the basic reproduction number, R0. This helps examine the dynamical behavior of the models and how vaccines can help prevent the spread of the virus.
AbstractThe role of mathematical models in engineering design is no longer that of simply automating techniques which were previously carried out manually. Throughout industry models are now becoming accepted as one of the main decision support systems to managers. This is certainly the case in engineering design for managing the environment. We are rapidly moving into the age of expert systems and hydro‐informatics, where the primary aim of most models is decision support. In this paper the role of the models in modern practice is reviewed and illustrated by case histories.