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The cacao swollen shoot virus disease (CSSVD) is among the most economically damaging diseases of cacao trees and accounts for almost 15–50% of harvest losses in Ghana. This virus is transmitted by several species of mealybugs (Pseudococcidae, Homoptera) when they feed on cacao plants. One of the mitigation strategies for CSSVD investigated at the Cocoa Research Institute of Ghana (CRIG) is the use of mild-strain cross-protection of cacao trees against the effects of severe strains. In this study, simple deterministic, delay, and stochastic ordinary differential equation-based models to describe the dynamic of the disease and spread of the virus are suggested. Model parameters are estimated using detailed empirical data from CRIG. The modeling outcomes demonstrate a remarkable resemblance between real and simulated dynamics. We have found that models with delay approximate the data better and this agrees with the knowledge that CSSVD epidemics develop slowly. Also, since there are large variations in the data, stochastic models lead to better results. We show that these models can be used to gain useful informative insights about the nature of disease spread. [ABSTRACT FROM AUTHOR]

We analyze the optimal lockdown in an economic–epidemic model with realistic infectiveness distribution. The model is described by Volterra integral equations and accurately depicts the COVID-19 infectivity pattern from clinical data. A maximum principle is derived, and a qualitative dynamic analysis of the optimal lockdown problem is provided over finite and infinite horizons. We analytically prove and economically justify the possibility of an endemic scenario when the infection rate begins to climb after the lockdown ends. [ABSTRACT FROM AUTHOR]

A nonlinear optimal control problem in the Lotka–McKendrick population model is studied. It describes rational management of age-structured farmed populations in aquaculture and indoor farms. Employing generalized functions, we prove the impulse nature of optimal harvesting. Exact analytic solutions for sustainable harvesting strategies are obtained and used to analyze the optimal dynamics of harvesting age and rotation under technological innovations. [ABSTRACT FROM AUTHOR]

We consider a nonlinear profit maximization problem in the Lotka–McKendrick model of age-structured harvested population describing farmed populations in agriculture and aquaculture. The control functions are time- and age-dependent harvesting rate and time dependent supply of newborns. We establish the existence of optimal controls with measure-valued harvesting rate by using distributional partial derivatives of functions of bounded variation through the equivalent integrated form to the original problem. [ABSTRACT FROM AUTHOR]

Habitat loss and harvesting of non-timber forest products (NTFPs) significantly affect the population dynamics. In this paper, we propose a general mathematical modelling approach incorporating the impact of habitat size reduction and non-lethal harvesting of NTFP on population dynamics. The model framework integrates experimental data of Pentadesma butyracea in Benin. This framework allows us to determine the rational non-lethal harvesting level and habitat size to ensure the stability of the plant ecosystem, and to study the impacts of distinct levels of humidity. We suggest non-lethal harvesting policies that maximize the economic benefit for local populations. [ABSTRACT FROM AUTHOR]

The integral model with finite memory is employed to analyze the timeline of COVID-19 epidemic in the United Kingdom and government actions to mitigate it. The model uses a realistic infection distribution. The time-varying transmission rate is determined from Volterra integral equation of the first kind. The authors construct and justify an efficient regularization algorithm for finding the transmission rate. The model and algorithm are approbated on the UK data with several waves of COVID-19 and demonstrate a remarkable resemblance between real and simulated dynamics. The timing of government preventive measures and their impact on the epidemic dynamics are discussed. [ABSTRACT FROM AUTHOR]

The paper focuses on modeling of public health measures to control the COVID‐19 pandemic. The authors suggest a flexible integral model with distributed lags, which realistically describes COVID‐19 infectiousness period from clinical data. It contains susceptible–infectious–recovered (SIR), susceptible–exposed–infectious–recovered (SEIR), and other epidemic models as special cases. The model is used for assessing how government decisions to lockdown and reopen the economy affect epidemic spread. The authors demonstrate essential differences in transition and asymptotic dynamics of the integral model and the SIR model after lockdown. The provided simulation on real data accurately describes several waves of the COVID‐19 epidemic in the United States and is in good correspondence with government actions to curb the epidemic. [ABSTRACT FROM AUTHOR]

Purpose: Despite the existence of multiple asset replacement theories, the economic life replacement method remains a major practical technique for making rational machine replacement decisions. The purpose of this paper is to bridge this method with comprehensive data analytic tools and make it applicable it to modern business reality with abundant data on operating and replacement costs. Design/methodology/approach: This study employs operations research, discrete and continuous optimization, applied mathematical modeling, data analytics, industrial economics and real options theory. Findings: Constructed stochastic algorithms extend the deterministic economic life method and are compared to the contemporary theory of stochastic asset replacement based on real options and dynamic programming. It is proven that both techniques deliver similar results when the cost volatility is small. A major theoretic finding is that the cost uncertainty speeds up the replacement decision. Research limitations/implications: This research suggests that the proposed stochastic algorithms may become an important tool for managerial decisions about replacement of many similar machines with detailed data on operating and replacement costs. Originality/value: Compared to the real options replacement theory, major advantages of the proposed algorithms are that they work equally well for any distribution of age-dependent stochastic operating cost. The algorithms are tested on a real industrial case about replacement of medical imaging devices. Numeric simulation supports obtained analytic outcomes. [ABSTRACT FROM AUTHOR]

We analyse the serial asset replacement problem under incomplete data about technological change that that affects the capital cost, operating cost and salvage value of newer assets. We construct an efficient discrete-time algorithm for this problem in the case where only partial information is available about future costs of new assets. The algorithm is based on introducing a corrected annual capital recovery factor into the classic Economic Life method. It produces the same lifetime of the first asset as the benchmark infinite-horizon cost minimisation when the operating cost, capital cost and salvage value of new assets decrease proportionally. The algorithm has the same complexity as the Economic Life method but performs much better under improving technology. Numeric simulation demonstrates a superior efficiency of the suggested algorithm vs. existing methods in practical situations when only few discrete measurements of technological change are available. [ABSTRACT FROM AUTHOR]

This paper studies the cost-minimizing serial asset replacement problem under changing operating and replacement costs. Technological improvements affect these costs in different ways, which leads to different duration of sequential replacement cycles of the same asset. Therefore, a firm should optimize a chain of consecutive asset replacements using available information about future costs. We offer a novel multi-cycle algorithm for making such replacement decisions and prove that it converges to the infinite-horizon solution when the number of cycles increases. Important qualitative properties of the obtained optimal non-equal-life replacement strategies are derived, and practical recommendations are discussed. [ABSTRACT FROM AUTHOR]

The review surveys and compares state-of-the-art epidemiologic models starting from the celebrated SIR model to recent SEIR Erlang models and integral models with distributed delays. The authors emphasize the flexibility and advantages of integral models in describing government efforts to control the current COVID -19 pandemic. [ABSTRACT FROM AUTHOR]

Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics. [ABSTRACT FROM AUTHOR]

Optimal asset replacement is analysed under non-exponential technological improvement, whereby the asset capital cost and the operational cost reduce for newer assets, and the relative rate of this decrease varies with time. We establish that the optimal lifetime of sequentially replaced assets increases if the relative rate of technological change decreases, and converse. Next, the two-cycle replacement algorithm is employed to take the unequal asset lifetime into account. The algorithm is adjusted to the case of several discrete estimates of changing asset costs and demonstrates good performance in various scenarios of improving technology. [ABSTRACT FROM AUTHOR]

An optimal control problem for nonlinear integral equations of special kind is analyzed. It considers a firm's investment into age-dependent capital under improving technology and limited substitutability among capital of different ages. We prove the existence of solutions and analyze their structure. It is shown that the initially bang-bang optimal investment switches to an interior one and eventually converges to a steady-state trajectory that represents balanced economic growth. The obtained analytic outcomes contribute to better understanding of investment policies under technological change. [ABSTRACT FROM AUTHOR]

We suggest analytic economic-environmental models that aim to investigate the multi-faced interplay between economic production, industrial pollution, and environmental protection. The considered static and dynamic optimization problems assess a country's sustainable environmental policy that involves the optimal combination of adaptation and mitigation strategies. A qualitative analysis of obtained solutions leads to relevant conclusions about the ranges of economic-environmental parameters, in which the adaptation and mitigation are viable policy options. [ABSTRACT FROM AUTHOR]

A hierarchical economic-environmental model is formulated to analyze the sustainable management of farming production in a landlord-tenant system. The problem under study is interdisciplinary and combines various agricultural, economic, social, and environmental factors. To maximize profit, the landlord chooses a rental payment and the duration of a lease contract. Tenants invest into farmyard fertilizer in order to improve future crop growth and maximize their profit. It is shown that the qualitative behavior of optimal trajectories in the landlord-tenant problem is mostly affected by environmental conditions rather than by the end-of-horizon and delay effects. A range of model parameters is identified, where the optimal trajectory coincides with the first-best environmentally and socially efficient solution. [ABSTRACT FROM AUTHOR]

We consider the optimal control of nonlinear integral equations with endogenous delay and state constraints, which describe a developing economy subjected to resource constraints. The economy invests in new resource-efficient technologies, invests in new capital, and scraps obsolete capital. We derive the optimality condition and determine long-term asymptotically exponential trajectories that optimally combine scrapping the dirtiest capital and developing new clean technologies. Next, we study the short-term dynamics of the model and show that it leads to a sustainable growth with active resource constraint. [ABSTRACT FROM AUTHOR]

Work significantly affects human life and health. Overworking may decrease the quality of life and cause direct economic losses. Technological innovations promote the modernization of firms' capital and lead to the improvement of labor productivity in the workplace. This paper investigates the optimal individual choice of work intensity under improving technology embodied in a new equipment. The balanced growth trajectories are obtained and analyzed to find their impact on the work-leisure balance problem and links between the optimal choice of work intensity and the rate of embodied technological change. [ABSTRACT FROM AUTHOR]

This paper performs a systematic study of some nonlinear integral equations with unknown lower limits of integration, which arise in economics, operations research, population biology and environmental sciences. A general investigation technique is developed for systems of such equations and several theorems about the existence and uniqueness of a solution are proven. The links to other functional equations with state-dependent delays are discussed. Applied interpretation of the obtained results is provided. [ABSTRACT FROM AUTHOR]

We perform the steady-state analysis of a nonlinear partial differential equation model that describes the dynamics of a managed size-structured forest. The harvesting policy is to maximize the net benefits from timber production over an infinite planning horizon. The existence and uniqueness of the steady-state trajectories are analysed. Closed-form steady states are obtained in meaningful special cases and are used to estimate how climate change affects the optimal harvesting regime, diameter of cut trees, number of logged trees, and net benefits in the long run. [ABSTRACT FROM AUTHOR]

The paper analytically explores the optimal allocation of investments into mitigation and environmental adaptation against climate change damages at a macroeconomic level. The economic-environmental model is formulated as a social planner problem where adaptation and abatement investments are separate decision variables. The existence of a unique steady state is proven. A comparative static analysis of optimal investments leads to essential implications for associated long-term environmental policies. It is shown that the optimal policy mix between adaptation and mitigation is lower for countries with higher economic efficiency for all applicable parameter ranges. Data calibration and numerical simulations are provided to estimate practical validity of theoretical outcomes. [ABSTRACT FROM AUTHOR]

The paper analyzes a fleet replacement problem under general assumptions about technological improvement. The corresponding optimization model considers the variable lifetime of assets in deterministic infinite-horizon settings. The optimal dynamics of the asset lifetime and investment is investigated analytically and numerically under continuous technological change and technological shocks that affect the operating and new asset costs. The obtained results contribute to the OR replacement theory and suggest simple rules for the efficient fleet replacement under improving technology. [ABSTRACT FROM AUTHOR]

The rational replacement management of hi-tech equipment is an important problem of technology management. This paper analyzes and compares two alternative policies for determining the service life and replacement demand of industrial equipment under improving technology. These policies lead to different estimates of the impact of new technology on the replacement policies and equipment service life. [ABSTRACT FROM AUTHOR]

Optimal control of partial differential equations arises in population ecology, economics, and demography. The consistency of mathematical treatment is demonstrated for the Lotka-McKendrick model and its nonlinear modifications of increasing complexity. The obtained qualitative optimal dynamics show that the models have either the bang-bang structure of optimal controls or follow balanced growth dynamics. [ABSTRACT FROM AUTHOR]

In operations research, the equipment replacement process is usually modeled in discrete time. An alternative approach is represented by continuous-time vintage capital models that explicitly involve the equipment lifetime and are described by nonlinear integral equations. The paper introduces and analyzes a model that unites both these approaches. The structure of optimal replacement, transition, and long-term dynamics, and clustering and splitting of replaced machines are discussed and illustrated with numeric examples. Equipment splitting is demonstrated when the optimal equipment lifetime increases. [ABSTRACT FROM AUTHOR]

The Kyoto protocol allows Annex I countries to deduct carbon sequestered by land use, land-use change, and forestry from their national carbon emissions. J. Thornley and M. Cannell (2000. Managing forests for wood yield and carbon storage: A theoretical study. Tree Physiol. 20:477- 484) have demonstrated that the objectives of maximizing timber and carbon sequestration are not complementary. Based on this finding, this article presents a model that takes into account the dynamics of timber and carbon in the form of an integro-partial differential and an ordinary differential equation. The integrated biophysical and economic model allows the optimal selective management regime to be determined. The results show that an increase in the carbon price leads to a notable increase in the number of trees. The findings also suggest that carbon sequestration costs are significantly lower for a change in a forest management regime than for a change in land use (afforestation). [ABSTRACT FROM AUTHOR]

The paper analyzes the optimal maintenance of a "fully manageable" biological population with no natural reproduction. Examples of such populations include dairy farms, horse breeding, gardening, and forestry. Mathematically, the problem leads to the nonlinear optimal control of a first-order partial differential equation with pointwise state constraints. A necessary extremum condition is proven using the abstract optimization theory in Banach spaces. It is shown that the optimal dynamics has a bang–bang structure with three jumps and involves buying new young individuals and selling the old ones when their anticipated future expenses exceed the profit. [ABSTRACT FROM AUTHOR]

The authors analyze the optimal replacement of a single asset under continuous and discontinuous technological change. They consider an infinite-horizon replacement problem with a variable asset lifetime. Due to deterioration, maintenance costs increase when the asset becomes older. Because of technological change, both maintenance and new capital costs decrease in time for a fixed asset age. The dynamics of the optimal asset lifetime are studied analytically and numerically in the cases of one and several technological breakthroughs. The breakthroughs cause irregularities (anticipation echoes) in the asset lifetime before the breakthrough time. It is shown that the optimal lifetime is always smaller when new capital costs decrease faster, when the maintenance costs decrease slower, or when both maintenance and new capital costs decrease faster with the same rate. [ABSTRACT FROM AUTHOR]

An exact solution is constructed to a nonlinear optimization problem in an integral dynamic model with delay. The problem involves the unknown duration of the delay and has important applications to the optimal replacement of capital equipment under technological change. [ABSTRACT FROM AUTHOR]

Optimization problems with nonlinear utility and endogenous capital lifetime are investigated in one- and two-sector modifications of the Solow vintage capital model. Both models have the same balanced growth path in the case of exponential technological change and labour. Turnpike theorems in normal form are proved for the optimal capital lifetime in both models. The differences between the cases of the linear and nonlinear utility are highlighted. [ABSTRACT FROM AUTHOR]

A model of the governmental control of age at retirement uses population age structures, productivity, employment, and money income. The sustainability criterion is a sufficient level of individual money income for all ages. The decision variables are the variable age at retirement and the intensity of technological change. The model is calibrated on real data from the U.S. Census Bureau and Bureau of Labor Statistics between 1950 and 2005 and uses official U.S. population projections for 2006-2050. The main result is that the extrapolation of current U.S. technological trends can compensate negative demographic trends in the United States without increasing the age at retirement. [ABSTRACT FROM AUTHOR]

The paper analyzes the problem of rational replacement of computing systems. Such systems, especially high-performance computers, are expensive, but quickly become obsolete. A system analysis of the replacement problem is provided and the relevant modeling problems are identified and studied. The obtained results give certain rules for calculating the optimal lifetime of computing systems, which are based on the given rates of technological change in the related computer industry. Two simulation examples estimate the optimal lifetime of PCs and high-performance computers in the current US economy. The results are in good agreement with other recommendations and existing business practice. [ABSTRACT FROM AUTHOR]