Optimal Birth Control Research Articles

Identifying the Optimal Birth Control for Patients

Despite decreases in pregnancy and abortion rates over the past few decades, unintended pregnancy remains a personal and public health challenge.1 In the 1960s, the first birth control pills (progestin only and combined) revolutionized contraceptive effectiveness despite their high estrogen doses. In the 1980s, safety became front of mind, as older intra-uterine devices (IUDs) and implants were removed from the market, leading to the development of newer, safer options we enjoy today. In the 1990s, pill-related venous thromboembolism (VTE) scares led to surges in unintended pregnancy rates in the United Kingdom and Europe, only to be repeated in the 2000s. In the 2010s, long-acting reversible contraception (LARC) was hailed as the path forward for reducing pregnancy rates and, indeed, this has contributed to modest reductions in unintended pregnancy and abortion rates. This decade has seen two major shifts in contraceptive care: the transition to blended models of service delivery (especially virtual and subscription-based options) and a transition toward “needs-based” counselling.

Analysis of diffusive size-structured population model and optimal birth control

<p style='text-indent:20px;'>This work addresses the optimal birth control problem for invasive species in a spatial environment. We apply the method of semigroups to qualitatively analyze a size-structured population model in which individuals occupy a position in a spatial environment. With insect population in mind, we study the optimal control problem which takes fertility rate as a control variable. With the help of adjoint system, we derive optimality conditions. We obtain the optimality conditions by fixing the birth rate on three different sets. Using Ekeland's variational principle, the existence, and uniqueness of optimal birth controller to the given population model which minimizes a given cost functional is shown. A concrete example is also given to see the behaviour of population density. Outcomes of our article are new and complement the existing ones.</p>

Optimal birth control problems for a nonlinear vermin population model with size-structure

In this paper we investigate theoretically the least cost-size problem and the least cost-deviation problem for a nonlinear size-structured vermin population model with separable mortality, which takes fertility rate as the control variable. We obtain the existence of a unique non-negative solution by considering the separable solution of the model, which is crucial to obtain the optimal control strategy. We also illustrate the continuous dependence of the population density on initial value and control parameter. Finally, we study the least cost-size problem and the least cost-deviation problem. Our conclusion would be useful for managing the vermin.

An optimal birth control problem for a dynamical population model with size-structure

This work is concerned with an optimal control problem for a size-structured population model, which takes fertility as the control variable. The existence and uniqueness of solutions to the basic state system and the dual system are proven via the Banach fixed point theorem. Necessary optimality conditions of first order are established in the form of an Euler–Lagrange system by the use of tangent–normal cone technique. The existence of a unique optimal controller is established by means of Ekeland’s variational principle. An example and some comments are presented.

Optimal birth control of free horizon problems for predator-prey system with age-structure

We study optimal birth policies for three age-dependent populations in a predator-prey system, which is controlled by fertility. New results on problems with free final time and integral phase constraints are presented, the approximate controllability of system is discussed.

Optimal birth control for competition system of three species with age-structure

In this paper, we investigate optimal policies for three age-dependent populations in a competition system, which is controlled by fertility. By using Dubovitskii-Milyutin's general theory, the maximum principles are obtained for problems with free terminal states, infinite horizon and target sets, respectively.

Optimal birth control of age-dependent competitive species III. Overtaking problem

A study is made of an overtaking optimal problem for a population system consisting of two competing species, which is controlled by fertilities. The existence of optimal policy is proved and a maximum principle is carefully derived under less restrictive conditions. Weak and strong turnpike properties of optimal trajectories are established.

Numerical solution to the optimal birth feedback control of a population dynamics: viscosity solution approach

AbstractThis paper is concerned with the optimal birth control of a McKendrick‐type age‐structured population dynamic system. We use the dynamic programming approach in our investigation. The Hamilton–Jacobi–Bellman equation satisfied by the value function is derived. It is shown that the value function is the viscosity solution of the Hamilton–Jacobi–Bellman equation. The optimal birth feedback control is found explicitly through the value function. A finite difference scheme is designed to obtain the numerical solution of the optimal birth feedback control. The validity of the optimality of the obtained control is verified numerically by comparing with different controls under the same constraint. All the data utilized in the computation are taken from the census of the population of China in 1989. Copyright © 2005 John Wiley & Sons, Ltd.

Optimal birth control of age-dependent competitive species: II. Free horizon problems

We study optimal birth policies for two age-dependent populations in a competing system, which is controlled by fertilities. New results on problems with free final time and integral phase constraints are presented, and the approximate controllability of system is discussed.

Optimal birth control of age-dependent competitive species

This work is concerned with optimal policies for two age-structured biological populations in a competing system, which is controlled by fertilities. The maximum principles for problems with free terminal, infinite horizon and target sets are obtained respectively via Dubovitskii–Milyutin's general extremal theory.

Optimal birth control problems for nonlinear age-structured population dynamics

We study the least cost-size problem and the least cost-deviation problem for a nonlinear population model with age-dependence, which takes fertility rate as the control variable. The existence of a unique optimal control and the optimality conditions of first order are investigated by means of Ekeland's variational principle and normal cone technique. Our conclusion extends a known result in the literature.

Optimal birth control for an age-dependent n-dimensional food chain model

In this paper, we investigate optimal policies for an age-dependent n-dimensional food chain model, which is controlled by fertility. By using Dubovitskii–Milyutin's general theory, the maximum principles are obtained for problems with free terminal states, infinite horizon and target sets, respectively.

Optimal birth control for predator–prey system of three species with age-structure

In this paper, we investigate optimal policies for three age-dependent populations in a predator–prey system, which is controlled by fertility. By using Dubovitskii–Milyutin's general theory, the maximum principles are obtained for problems with free terminal states, infinite horizon and target sets, respectively.

Bone-sparing properties of oral contraceptives

Postmenopausal osteoporosis is a major health care problem that affects 20 million women in the United States and accounts for >1 million fractures per year. Hormone replacement therapy is effective for reducing bone loss in the postmenopausal women. However, intervention before menopause may delay or prevent the decline in bone mass that begins between ages 30 and 40 years. The effects of oral contraceptives on bone mass have been investigated, and a positive association between oral contraceptive use and bone mass that is directly related to the duration of oral contraceptive use was observed. The effects of oral contraceptives on bone mass may be related to the specific formation. The effect of estrogens is dose related, and the optimal dose appears to be 25 to 35 μg of ethinyl estradiol or its equivalent. Results from several studies show that norethindrone has a positive effect on bone mass. An oral contraceptive may offer optimal birth control for the older premenopausal woman who currently uses other forms of birth control. (A M J O BSTET G YNECOL 1996;174:15-20.)

Overtaking optimal control problem of age-dependent populations with infinite horizon

The optimal birth control of an age-dependent population model with unbounded time interval is considered. The minimum principle which must be satisfied by the overtaking optimal control is established. Large time behaviour and the turnpike property of the overtaking optimal trajectory are studied. Existence results are also presented.

Optimal birth control of population dynamics. II. Problems with free final time, phase constraints, and mini-max costs

We study optimal birth control of population systems of McKendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control. New results on problems with free final time, phase constraints, and mini-max costs are presented.

Optimal birth control of population dynamics

We study optimal birth control policies for an age-structured population of McKendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control. The functional analytic approach of Dubovitskii and Milyutin is adopted in the investigation. Maximum principles for problems with a free end condition a fixed final horizon are developed, and the time optimal control problem, the problem with target sets, and the infinite planning horizon case are investigated.

Pontryagin's principle for control problems in age-dependent population dynamics.

In this paper, Pontryagin's principle is proved for a fairly general problem of optimal control of populations with continuous time and age variable. As a consequence, maximum principles are developed for an optimal harvesting problem and a problem of optimal birth control.