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Fractional-Order Model for Myxomatosis Transmission Dynamics: Significance of Contact, Vector Control and Culling
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | A fractional-order model for myxomatosis transmission dynamics is developed and analyzed. The presented compartmentalized model is based on the Caputo--Fabrizio fractional-order type owing to its flexibility when handling initial value problems. The model properties such as positivity and boundedness are proved using a one-parameter Mittag--Leffler function approximation. The model reproduction number, R0, is determined using the next-generation method assuming the integer-order case of the model and is used to determine the conditions for disease progression as well as its containment. Furthermore, the existence and uniqueness of nontrivial solutions of the model are shown using the fixed point theory. In addition, we performed sensitivity analysis of model parameters as inputs with R0 as the output using the Latin hypercube sampling (LHS) scheme and determined the key processes that must be targeted in order to contain the infection. The significance of parameter values was based on ????-values obtained after performing Fisher-transformation on the obtained partial rank correlation coefficients. More still, pairwise comparison of significant parameters was carried out with and without false discovery rate adjustment to ensure that significantly different processes are not falsely disqualified. Our results show that the model has a locally asymptotically stable disease-free equilibrium when R0 is less than one and a unique endemic equilibrium whenever R0 is greater than one. The sensitivity analysis process revealed that on one hand, the processes described by parameters related to contact have the greatest potential of making the epidemic worse if not curtailed. On the other hand, the processes associated with recovery of rabbits are highly vital in containing the disease when enhanced. Although the obtained median of the reproduction number is around 1, we observe that while there are combinations of parameters that can make the infection worse, there are also combinations that can be enhanced to curtail the infection. We further observed that increased memory/dependence of future values of the model on previous states predicts lower peak values of infected cases in the short-term but higher equilibrium values in the long-term. Based on our results, we recommend that infected rabbits be isolated to reduce contact with uninfected ones. Furthermore, efforts must be put in place to minimize the contact between the vectors and rabbits as well as reduce the vector population if the disease is to be contained. In the worst-case scenario, culling of infected rabbits can be applied to reduce the likelihood of transmission through contact between susceptible and infected rabbits. |
Probabilistic Gathering of Agents with Simple Sensors
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | Gathering is a fundamental task for multiagent systems. The problem has been studied under various assumptions on the sensing capabilities of mobile agents. This paper addresses the problem for a group of agents that are identical and indistinguishable, oblivious, and lack the capacity of direct communication. At the beginning of unit time-intervals, the agents select random headings in the plane and then detect the presence of other agents behind them. Then they move forward only if no agents are detected in their sensing “back half-plane.” Two types of motion are considered: when no peers are detected behind them, either the agents perform unit jumps forward, or they start to move with unit speed while continuously sensing their back half-plane, and stop whenever another agent appears there. For the first type of motion extensive empirical evidence suggests that with high probability clustering occurs in finite expected time to a small region with diameter of about the size of the unit jump, while for continuous sensing and motion we can prove gathering in finite expected time if a “blind-zone” is assumed in their sensing half-plane. Relationships between the number of agents or the size of the blind-zone and convergence time are empirically studied and compared to a theoretical upper-bound dependent on these factors. |
A Homogenized Model for a Reactive Filter
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | Abstrak tidak tersedia. |
Predicting Lift-Off Time When Deep-Frying Potato Dough Snacks
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | When frying potato snacks, it is typically observed that the dough, which is submerged in hot oil, after some critical time increases its buoyancy and floats to the surface. The lift-off time is a useful metric in ensuring that the snacks are properly cooked. Here we propose a multiphase mathematical model for the frying of potato snacks, where water inside the dough is evaporated from both the top and bottom surfaces of the snack at two receding evaporation fronts. The vapor created at the top of the snack bubbles away to the surface, whereas the vapor released from the bottom surface forms a buoyant blanket layer. By asymptotic analysis, we show that the model simplifies to solving a one-dimensional Stefan problem in the snack coupled to a thin-film equation in the vapor blanket through a nonlinear boundary condition. Using our mathematical model, we predict the change in the snack density as a function of time and investigate how lift-off time depends on the different parameters of the problem. |
Theorems on the Stokesian Hydrodynamics of a Rigid Filament in the Limit of Vanishing Radius
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | The transport dynamics of a rigid filament in a slow viscous flow modeled by the Stokes equations in a three-dimensional domain are considered. The relation between the transport velocities, external loads, and far-field flow around the filament is studied in the singular limit as the radius of the filament tends to zero, and the filament collapses to a curve, which may be an open arc or closed loop. Beginning from an initially implicit relation defined through the solution of a boundary-value problem, a potential theoretic representation is used to show that the relation between the transport velocities, external loads, and far-field flow remains well defined and remarkably becomes explicit in the limit of vanishing radius. Theorems establishing the form of this relation in different cases are stated, proved, and illustrated with examples. Special considerations at the ends of the filament when the limiting curve is open are discussed throughout. |
The Necessary Modeling Detail for Neuronal Signaling: Poisson--Nernst--Planck and Cable Equation Models in One and Three Dimensions
| Pengarang | : | Markus Breit |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | Modeling and simulation of neuronal processes has evolved from the one-dimensional (1D), symmetry-exploiting cable equation to detailed 3D models that incorporate the ultrastructural architecture of neurons. While dimension-reduced models have the clear advantage of simplicity, which makes numerical simulation an easy task, they neglect structural details which may be relevant when studying the structure-function interplay in cells. The Poisson--Nernst--Planck equations represent the other end of the modeling spectrum, a continuum mechanics model that accounts for the 3D domain as well as the spatio-temporal ion concentrations involved in biochemical signaling. In the presented work, we show that three simpler models can be derived from the Poisson--Nernst--Planck equations: the broadly used 1D cable equation, a 3D version thereof, and a 1D electro-diffusion model. We identify the assumptions and approximations that are made for the simpler models and, using numerical simulation, assess the impact of violations of these assumptions on model accuracy in scenarios ranging from individual axon fibers and bundles to dendritic spine microdomains. It is shown that the coarsest model (1D cable equation) is able to accurately resolve the electric behavior in all scenarios, as long as the cellular geometry does not diverge significantly from symmetric local cylinders. In cases where the ionic spatio-temporal dynamics are relevant, more detailed models like the 3D Poisson--Nernst--Planck equations need to be employed. We conclude with guidelines as to which level of modeling detail is necessary to capture the underlying neurobiological features accurately. |
On the Relation between the Lifshitz--Slyozov and the Lifshitz--Slyozov--Wagner Models for Supersaturated Solutions
| Pengarang | : | Giulio Lauretano |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | The Lifshitz--Slyozov (LS) and the Lifshitz--Slyozov--Wagner (LSW) models for the so-called “Ostwald ripening" are compared, with the purpose to test the limits of validity of the approximation that the LSW model is expected to represent for the LS model. The generally nonmonotonic behavior of the monomers' concentration is discussed and shown in a few examples. An asymptotic approach is followed to justify theoretically the aforementioned approximation. Illustrative examples are given. |
Inverse Random Source Scattering for the Helmholtz Equation with Attenuation
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a classical pseudodifferential operator. The work contains three contributions. First, the connection is established between fractional Gaussian fields and rough sources characterized by their principal symbols. Second, the direct source scattering problem is shown to be well-posed in the distribution sense. Third, we demonstrate that the micro-correlation strength of the random source can be uniquely determined by the passive measurements of the wave field in a set which is disjoint with the support of the strength function. The analysis relies on careful studies on the Green function and Fourier integrals for the Helmholtz equation. |
A Gravity Current Model with Capillary Trapping for Oil Migration in Multilayer Geological Basins
| Pengarang | : | David Maltese |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | We propose a reduced model taking account of the capillary trapping to simulate oil migration in geological basins made of several rock types. Our model is derived from Darcy type models thanks to Dupuit approximation and a vertical integration in each geological layer. We propose a time-implicit finite volume scheme which is shown to be unconditionally stable and to admit discrete solutions. Numerical outcomes are then provided in order to illustrate the behavior of our reduced model. |
Modeling the Emergence of Phenotypic Heterogeneity in Vascularized Tumors
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 81 (No. 2) |
| Halaman | : | |
| Abstrak | : | We present a mathematical study of the emergence of phenotypic heterogeneity in vascularized tumors. Our study is based on formal asymptotic analysis and numerical simulations of a system of nonlocal parabolic equations that describes the phenotypic evolution of tumor cells and their nonlinear dynamic interactions with the oxygen, which is released from the intratumoral vascular network. Numerical simulations are carried out both in the case of arbitrary distributions of intratumor blood vessels and in the case where the intratumoral vascular network is reconstructed from clinical images obtained using dynamic optical coherence tomography. The results obtained support a more in-depth theoretical understanding of the eco-evolutionary process which underpins the emergence of phenotypic heterogeneity in vascularized tumors. In particular, our results offer a theoretical basis for empirical evidence indicating that the phenotypic properties of cancer cells in vascularized tumors vary with the distance from the blood vessels, and establish a relation between the degree of tumor tissue vascularization and the level of intratumor phenotypic heterogeneity. |