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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]

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]

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]

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]

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]