Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.

https://epubs.siam.org/doi/pdf/10.1137/S0036144500371907

The Mathematics of Infectious Diseases

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

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

/pdf/differential-equations-and-dynamical-systems-3chsjx2k45.pdf

Differential Equations and Dynamical Systems

The reemergence of tuberculosis (TB) from the 1980s to the early
1990s instigated extensive researches on the mechanisms behind the
transmission dynamics of TB epidemics. This article provides a
detailed review of the work on the dynamics and control of TB. The
earliest mathematical models describing the TB dynamics appeared in
the 1960s and focused on the prediction and control strategies using
simulation approaches. Most recently developed models not only pay
attention to simulations but also take care of dynamical analysis
using modern knowledge of dynamical systems. Questions addressed by
these models mainly concentrate on TB control strategies, optimal
vaccination policies, approaches toward the elimination of TB in the
U.S.A., TB co-infection with HIV/AIDS, drug-resistant TB, responses
of the immune system, impacts of demography, the role of public
transportation systems, and the impact of contact patterns. Model
formulations involve a variety of mathematical areas, such as ODEs
(Ordinary Differential Equations) (both autonomous and
non-autonomous systems), PDEs (Partial Differential Equations),
system of difference equations, system of integro-differential
equations, Markov chain model, and simulation models.

Dynamical models of tuberculosis and their applications.

Want to get experience? Want to get any ideas to create new things in your life? Read methods of numerical integration now! By reading this book as soon as possible, you can renew the situation to get the inspirations. Yeah, this way will lead you to always think more and more. In this case, this book will be always right for you. When you can observe more about the book, you will know why you need this.

Methods of Numerical Integration

A semi-discrete finite element method requiring only continuous element is presented for the approximation of the solution of the evolutionary, fourth order in space, Cahn-Hilliard equation. Optimal order error bounds are derived in various norms for an implementation which uses mass lumping. The continuous problem has an energy based Lyapunov functional. It is proved that this property holds for the discrete problem.

A second order splitting method for the Cahn-Hilliard equation

A mixed finite element method is developed to approximate the solution of a quasilinear second-order elliptic partial differential equation. The existence and uniqueness of the approximation are demonstrated and optimal rate error estimates are derived.

Mixed finite element methods for quasilinear second-order elliptic problems

Long periods of latency and the emergence of antibiotic resistance due to incomplete treatment are very important features of tuberculosis (TB) dynamics. Previous studies of two-strain TB have been performed by ODE models. In this article, we formulate a two-strain TB model with an arbitrarily distributed delay in the latent stage of individuals infected with the drug-sensitive strain and look at the effects of variable periods of latency on the disease dynamics.

A two-strain tuberculosis model with age of infection ∗

A model which describes the dynamics of an $S \to I \to S$ epidemic in an age-structured population at the steady state is considered. The model consists of a nonlinear and nonlocal system of equations of hyperbolic type and has already been partly analyzed by other authors. Here, a special form for the force of infection is considered. Explicitly computable threshold conditions are given, and some regularity results for the solutions are proven. An implicit finite difference method of characteristics to approximate the solutions is used. Optimal error estimates are derived and results from numerical simulations are presented. The discrete dynamical system arising from the numerical algorithm, is also analyzed, showing that it shares many properties of the continuous model.

Analytical and numerical results for the age-structured S-I-S epidemic model with mixed inter-intracohort transmission

shmoop. age structured population dynamics in demography and. population age distribution britannica. three basic epidemiological models mount holyoke college. age structure population growth and economic development. age structured leslie matrix theory population ecology. age stage classified demographic analysis a. analysis of age structured population models with an. unit 2 age structure diagrams quiz quizizz. population dynamics of fisheries. predicting human population change part 1 age structure. how reproductive age groups impact age structure diagrams. population aging longevity science. key concept populations have many characteristics. the effects of age structure on development policy and. leslie matrix. aging productivity and innovation aging and the. the basic approach to age structured population dynamics. age structured population encyclopedia of mathematics. what is a bank street approach to preschool sheknows. ap environmental science chapter 3 flashcards quizlet. 6 population models and evaluation of models using. the basic approach to age structured population dynamics. age structured models in population dynamics and economics. what is population structure reference. population growth analysis of an age structure population. age structured matrix population models. population pyramid sociology britannica. mathematical analysis of an age structured sir epidemic. the basic approach to age structured population dynamics. covid 19 mortality highly influenced by age demographics. an age structured population model. population biology amp human population questions and study. population ecology 1 biology 1510 biological principles. age structure and age pyramids thoughtco. population characteristics 5 important characteristics of. a continuous time age structured population growth model. chapter 1 population growth and economic development. analysis and numerics for an age and sex structured. evaluation and analysis of age and sex structure. the basic approach to age structured population dynamics. age sex and population pyramids thoughtco. what is the important of age structure in population studies. population size density amp dispersal article khan academy. global population age structures and sustainable development

Fabio A. Milner

Papers

A second order splitting method for the Cahn-Hilliard equation

Mixed finite element methods for quasilinear second-order elliptic problems

A two-strain tuberculosis model with age of infection ∗

Analytical and numerical results for the age-structured S-I-S epidemic model with mixed inter-intracohort transmission

The Basic Approach to Age-Structured Population Dynamics