OPAC - Pencarian Artikel Jurnal & Majalah Library USD
Menampilkan semua artikel (Halaman 557 dari 34170, Total: 341698 data)
OPTIMAL INTERVENTION STRATEGIES FOR MINIMIZING TOTAL INCIDENCE DURING AN EPIDEMIC
klik untuk membaca file PDF
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 2) |
| Halaman | : | 354-373 |
| Abstrak | : | This article considers the minimization of the total number of infected individuals over the course of an epidemic in which the rate of infectious contacts can be reduced by time dependent nonpharmaceutical interventions. The societal and economic costs of interventions are taken into account using a linear budget constraint which imposes a trade-off between short-term heavy interventions and long-term light interventions. We search for an optimal intervention strategy in an infinite-dimensional space of controls containing multiple consecutive lockdowns, gradually imposed and lifted restrictions, and various heuristic controls based, for example, on tracking the effective reproduction number. Mathematical analysis shows that among all such strategies, the global optimum is achieved by a single constant-level lockdown of maximum possible magnitude. Numerical simulations highlight the need for careful timing of such interventions and illustrate their benefits and disadvantages compared to strategies designed for minimizing peak prevalence. Rather counterintuitively, adding restrictions prior to the start of a well-planned intervention strategy may even increase the total incidence. |
SELECTIONMECHANISMINNON-NEWTONIAN SAFFMAN-TAYLORFINGERS
| Pengarang | : | Bansal, Diksha,Ghosh, Dipa,Sircar, Sarthok |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 2) |
| Halaman | : | 329-353 |
| Abstrak | : | \mathrm{W}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{y}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{a}\mathrm{c}\mathrm{h}\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{m}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\mathrm{e}fi\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{f} \mathrm{a}\mathrm{s}\mathrm{i}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}fl\mathrm{u}\mathrm{i}\mathrm{d}\mathrm{d}\mathrm{r}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{N}\mathrm{e}\mathrm{w}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{n}(\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}-\mathrm{l}\mathrm{a}\mathrm{w})fl\mathrm{u}\mathrm{i}\mathrm{d}. \mathrm{O}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{y}\mathrm{s}\mathrm{i}\mathrm{s} \mathrm{i}\mathrm{s}\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{W}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{z}\mathrm{e}\mathrm{l} \mathrm{K}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}-\mathrm{B}\mathrm{r}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{u}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{x}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}, \mathrm{b}\mathrm{y}\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{v}\mathrm{i}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{N}\mathrm{e}\mathrm{w}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{v}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{a}\mathrm{s} \mathrm{a}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{i}\mathrm{n}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}, \mathrm{l}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{o}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{v}\mathrm{a}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e}fi\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{r} \mathrm{t}\mathrm{i}\mathrm{p},\mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h} \mathrm{s}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{s}\mathrm{a}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{q}\mathrm{u}\mathrm{e}fi\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{f}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{l}\mathrm{y}\mathrm{o}\mathrm{f} \mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}. \mathrm{W}\mathrm{e}fi\mathrm{n}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t} \mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{d}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{s}fi\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h},\Lambda ,\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{o}\mathrm{f}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{v}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{a}\mathrm{n}\mathrm{d} \mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n},\nu ,\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\Lambda \sim 1 2 - \scrO (\nu - 1/2)\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{i}\mathrm{n}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{d}\Lambda \sim 1 2+\scrO (\nu 2/(4 - n)) \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{k}\mathrm{e}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{e}, \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{l}\nu .\mathrm{T}\mathrm{h}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{e} \mathrm{e}\mathrm{x}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{l},fi\mathrm{n}\mathrm{g}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{a}\mathrm{s}\mathrm{w}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l},\mathrm{a}\mathrm{n}\mathrm{d} \mathrm{a}\mathrm{g}\mathrm{o}\mathrm{o}\mathrm{d}\mathrm{a}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{s}\mathrm{f}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}\mathrm{n}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}-\mathrm{l}\mathrm{a}\mathrm{w}\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{n}\mathrm{t},n=1. |
ERRATUM: CLASSICAL AND QUANTUM RANDOM-WALK CENTRALITY MEASURES IN MULTILAYER NETWORKS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 327-328 |
| Abstrak | : | This erratum clarifies that equations (4.21) and (4.23) in B\"ottcher and Porter [SIAM J. Appl. Math., 81 (2021), pp. 2704-2724] assume that the underlying evolution operator has an orthonormal basis. The results and conclusions of the paper are unaffected by this clarification. |
UNIQUENESS IN INVERSE DIFFRACTION GRATING PROBLEMS WITH INFINITELY MANY PLANE WAVES AT A FIXED FREQUENCY
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 302-326 |
| Abstrak | : | This paper is concerned with uniqueness of solution of the inverse diffraction by problems by a periodic curve with Dirichlet boundary condition in two dimensions. It is proved that the periodic curve can be uniquely determined by the near-field measurement data corresponding to infinitely many incident plane waves with distinct directions at a fixed frequency. Our proof is based on Schiffer's idea which consists of two ingredients: (i) the total fields for incident plane waves with distinct directions are linearly independent, and (ii) for a fixed wave number there exist only finitely many linearly independent Dirichlet eigenfunctions in a bounded domain or in a closed waveguide under additional assumptions on the waveguide boundary. Based on the Rayleigh expansion, we prove that the phased near-field data can be uniquely determined by the phaseless near-field data in a bounded domain, with the exception of a finite set of incident angles. Such a phase retrieval result leads to a new uniqueness result for the inverse grating diffraction problem with phaseless near-field data at a fixed frequency. Since the incident direction determines the quasi-periodicity of the boundary value problem, our inverse issues are different from the existing results of [F. Hettlich and A. Kirsch, Inverse Problems, 13 (1997), pp. 351-361], where fixed-direction plane waves at multiple frequencies were considered |
DELAYED MODEL FOR THE TRANSMISSION AND CONTROL OF COVID-19 WITH FANGCANG SHELTER HOSPITALS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 276-301 |
| Abstrak | : | The ongoing coronavirus disease 2019 (COVID-19) pandemic poses a huge threat to global public health. Motivated by China's experience of using Fangcang shelter hospitals (FSHs) to successfully combat the epidemic in its initial stages, we present a two-stage delay model considering the average waiting time of patients' admission to study the impact of hospital beds and centralized quarantine on mitigating and controlling of the outbreak. We compute the basic reproduction number in terms of the hospital resources and perform a sensitivity analysis of the average waiting times of patients before admission to the hospitals. We conclude that, while designated hospitals save lives in severely infected individuals, the FSHs played a key role in mitigating and eventually curbing the epidemic. We also quantified some key epidemiological indicators, such as the final size of infections and deaths, the peak height and its timing, and the maximum occupation of beds in FSHs. Our study suggests that, for a jurisdiction (region or country) still struggling with COVID-19, when possible, it is essential to increase testing capacity and use a centralized quarantine to massively reduce the severity and magnitude of the epidemic that follows. |
AN EULERIAN NONLINEAR ELASTIC MODEL FOR COMPRESSIBLE AND FLUIDIC TISSUE WITH RADIALLY SYMMETRIC GROWTH
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 254-275 |
| Abstrak | : | Cell proliferation, apoptosis, and myosin-dependent contraction can generate elastic stress and strain in living tissues, which may be dissipated by internal rearrangement through cell topological transition and cytoskeletal reorganization. Moreover, cells and tissues can change their sizes in response to mechanical cues. The present work demonstrates the role of tissue compressibility and internal rearranging activities on its size and mechanics regulation in the context of differential growth induced by a field of growth-promoting chemical factors. We develop a mathematical model based on finite elasticity and growth theory and the reference map techniques to describe the coupled tissue growth and mechanics in the Eulerian frame. We incorporate the tissue rearrangement by introducing a rearranging rate to the reference map evolution, leading to elastic-energy dissipation when tissue growth and deformation are in radial symmetry. By linearizing the model, we show that the stress follows the Maxwell-type viscoelastic relaxation. The rearrangement rate, which we call tissue fluidity, sets the stress relaxation time, and the ratio between the shear modulus and the f luidity sets the tissue viscosity. By nonlinear simulation of growing tissue spheroids and discs with graded growth rates along the radius, we find that the tissue compressibility and fluidity influence their equilibrium size. By comparing the nonlinear simulations with the linear analytical solutions, we show the size change as a nonlinear effect due to the advection of the tissue density flow, which only occurs when both tissue compressibility and fluidity are small. We apply the model to study tumor spheroid growth and epithelial disc growth when a reaction-diffusion process determines the growth-promoting factor field. |
GRADIENT FLOWS FOR COUPLING ORDER PARAMETERS AND MECHANICS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 225-253 |
| Abstrak | : | We construct a formal gradient flow structure for phase-field evolution coupled to mechanics in Lagrangian coordinates, present common ways to couple the evolution, and provide an incremental minimization strategy. While the usual presentation of continuum mechanics is intentionally brief, we construct an extensible functional analytical framework and a discretization approach that preserves the underlying variational structure. We consider phase separation and swelling of gels and then study stationary states of multiphase systems with surface tension and contact lines and show the robustness of the general approach for large deformations. We highlight differences between compressible and incompressible models and discuss issues of the sharp-interface limit for different magnitudes of the Cahn-Hilliard mobility. |
FRONT PROPAGATION AND ARRIVAL TIMES IN NETWORKS WITH APPLICATION TO NEURODEGENERATIVE DISEASES
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 194-224 |
| Abstrak | : | Many physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key problem is then to extract estimates for the dynamics. In particular, if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? Here, motivated by the study of toxic protein propagation in neurodegenerative diseases, we present and compare three different estimates for the arrival time in order of increasing analytical complexity: the linear arrival time, obtained by linearizing the underlying dynamical system; the Lambert time, obtained by considering the interaction of pairs of nodes; and the nonlinear arrival time, obtained by asymptotic techniques. We use the classic Fisher-Kolmogorov-Petrovsky Piskunov equation as a paradigm for the dynamics and show that each method provides different insights but consistent time estimates. Further, we show that the nonlinear asymptotic method also gives an approximate solution, valid in the entire domain, and the correct ordering of arrival regions over large regions of parameters and initial conditions. |
ASYMPTOTIC PROPERTIES OF A GENERAL MODEL OF IMMUNE STATUS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 172-193 |
| Abstrak | : | We consider a model of dynamics of the immune system. The model is based on three factors: occasional boosting and continuous waning of immunity and a general description of the period between subsequent boosting events. The antibody concentration changes according to a non-Markovian process. The density of the distribution of this concentration satisfies some partial differential equation with an integral boundary condition. We check whether this system generates a stochastic semigroup and we study the long-time behavior of this semigroup. In particular we prove a theorem on its asymptotic stability. |
MODELING AND OPTIMAL CONTROL OF A TWO-SPECIES BIOPRODUCING MICROBIAL CONSORTIUM
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 1) |
| Halaman | : | 144-171 |
| Abstrak | : | Motivated by recent laboratory experiments, we study microbial populations with light-inducible genetic differentiation that generates a two-species microbial consortium relevant for bioproduction. First, we derive a hierarchy of models describing the evolution of the microbial populations, each with decreasing complexity. This sequential order reduction reveals the connections between several popular classes of models used in this context. Second, we demonstrate the analytical insight the order reduction provides by studying the optimal control of such a reduced-order system of nonlinear ordinary differential equations. Appealing to Pontryagin's maximum principle, we find different optimal control structures within different regions of the parameter space. Explicit solutions are obtained in a subset of parameter space, while, for the remainder of parameter space, closed-form solutions are obtained that depend on a scalar value that solves a particular transcendental equation. We show that a unique solution of the scalar equation exists and lies in a known compact interval, making its numerical approximation particularly easy. The analytical results are verified against direct numerical calculations |