By Matthew James Keelingand Pejman RohaniPrinceton, NJ: Princeton University Press,2008.408 pp., Illustrated. $65.00 (hardcover).Mathematical modeling of infectious dis-eases has progressed dramatically over thepast 3 decades and continues to ﬂourishat the nexus of mathematics, epidemiol-ogy, and infectious diseases research. Nowrecognized as a valuable tool, mathemat-ical models are being integrated into thepublic health decision-making processmore than ever before. However, despiterapid advancements in this area, a formaltraining program for mathematical mod-eling is lacking, and there are very fewbooks suitable for a broad readership. Tosupport this bridging science, a commonlanguage that is understood in all con-tributing disciplines is required.

Modeling Infectious Diseases in Humans and Animals

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.

Fixed Point Theory

computational fluid mechanics and heat transfer is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the computational fluid mechanics and heat transfer is universally compatible with any devices to read.

Computational Fluid Mechanics And Heat Transfer

Reviews - Eigenfunction Expansions Associated with Second-Order Differential Equations. By E. C. Titchmarsh Pp. 175. 20s. 1946. (Oxford University)

A SEIR model for the transmission of an infectious disease that spreads in a population through direct contact of the hosts is studied The force of infection is of proportionate mixing type A threshold sigma is identified which determines the outcome of the disease; if sigma 1, the infected fraction persists and a unique endemic equilibrium state is shown, under a mild restriction on the parameters, to be globally asymptotically stable in the interior of the feasible region Two other threshold parameters sigma' and sigma are also identified; they determine the dynamics of the population sizes in the cases when the disease dies out and when it is endemic, respectively

Global dynamics of a SEIR model with varying total population size.

On the generalized Liénard equation with negative damping

We treat the existence of multiple positive solutions for a third order boundary value problem with nonlocal boundary conditions. In our work, each of the three boundary conditions is a linear functional on C[0,1], that is, given by a Stieltjes integral, but is not necessarily a positive functional.

Third order boundary value problems with nonlocal boundary conditions

The authors consider the higher order boundary-value problem u (n) (t) = q(t)f(u(t)), 0 t 1, where n 4 is an integer, and p 2 (1/2,1) is a constant. Sucient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.

/pdf/positive-solutions-of-a-nonlinear-higher-order-boundary-4veqgmw1ro.pdf

John R. Graef

Papers

Global dynamics of a SEIR model with varying total population size.

On the generalized Liénard equation with negative damping

Third order boundary value problems with nonlocal boundary conditions

Positive solutions of a nonlinear higher order boundary-value problem

Positive solutions to a multi-point higher order boundary value problem