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Bifurcation Analysis of a Stochastic Phytoplankton Growth Model Under Photoinhibition
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| Pengarang | : | Da Song, Wentao Fu, Meng Fan |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 875-895 |
| Abstrak | : | This study is devoted to exploring the effects of photoinhibition and environmental stochasticity on the population dynamics of phytoplankton in a stochastic environment by a dynamical modeling approach. A stochastic model with photoinhibition is formulated to characterize the growth of phytoplankton, where the random disturbance is modeled by the multiplicative Gaussian white noise. The global dynamics of the model is well investigated both analytically and numerically. In particular, the stochastic bifurcation analysis is thoroughly examined and sufficient criteria are derived for the occurrence of phenomenological and dynamical bifurcations. The main findings indicate that photoinhibition can lead to a strong Allee effect in phytoplankton, as evidenced by the emergence of a stable bimodal limit distribution in the stochastic dynamical model. |
The Carleman Contraction Mapping Method for a Coefficient Inverse Problem of the Epidemiology
| Pengarang | : | Michael V. Klibanov, Trung Truong |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 848-874 |
| Abstrak | : | It is proposed to monitor spatial and temporal spreads of epidemics via solution of a coefficient inverse problem for a system of three coupled nonlinear parabolic equations. To solve this problem numerically, a version of the so-called Carleman contraction mapping method is developed for this problem. On each iteration, a linear problem with the incomplete lateral Cauchy data is solved by the weighted quasi-reversibility method, where the weight is the Carleman weight function. This is the function, which is involved as the weight in the Carleman estimate for the corresponding parabolic operator. Convergence analysis ensures the global convergence of this procedure. Numerical results demonstrate an accurate performance of this technique for noisy data. |
A Modified Landau–de Gennes Theory for Smectic Liquid Crystals: Phase Transitions and Structural Transitions
| Pengarang | : | Baoming Shi, Yucen Han, Chengdi Ma, Apala Majumdar, Lei Zhang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 821-847 |
| Abstrak | : | We mathematically model smectic-A (SmA) phases with a modified Landau–de Gennes (mLdG) model as proposed in Xia et al. [Phys. Rev. Lett., 126 (2021), 177801]. The orientational order of the SmA phase is described by a tensor-order parameter ?, and the positional order is described by a real scalar ?, which models the deviation from the average density of liquid crystal molecules. First, we prove the existence and regularity of global minimizers of the mLdG free energy in three-dimensional settings. Then we analytically prove that the mLdG model can capture the isotropic-nematic-smectic phase transition as a function of temperature, under some assumptions. Further, we explore stable smectic phases on a square domain with edge length ? and tangent boundary conditions. We use heuristic arguments to show that defects repel smectic layers and that nematic ordering promotes layer formation. We use asymptotic arguments in the ?→0 and ?→∞ limits which reveal the correlation between the number and thickness of smectic layers, the amplitude of density fluctuations with the phenomenological parameters in the mLdG energy. For finite values of ?, we numerically recover BD-like and D-like stable smectic states observed in experiments. We also study the frustrated mLdG energy landscape and give numerical examples of transition pathways between distinct mLdG energy minimizers. |
Vaccinating According to the Maximal Endemic Equilibrium Achieves Herd Immunity
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 806-820 |
| Abstrak | : | We consider the simple epidemiological SIS model for a general heterogeneous population introduced by Lajmanovich and Yorke (1976) in finite dimensions, and its infinite-dimensional generalization we introduced in previous works. In this model the basic reproducing number ?0 is given by the spectral radius of an integral operator. If the basic reproducing number ?0 is greater than 1 (?0>1), then there exists a maximal endemic equilibrium. In this very general heterogeneous SIS model, we prove that vaccinating according to the profile of this maximal endemic equilibrium ensures herd immunity. Moreover, this vaccination strategy is critical: the resulting effective reproduction number is exactly equal to one. As an application, we estimate in an example from Britton, Ball, and Trapman (2020) that if ?0=2 in an age-structured community with mixing rates fitted to social activity, applying this strategy would require approximately 29% fewer vaccine doses than the strategy which consists in vaccinating uniformly a proportion 1−1/?0 of the population. From a dynamical systems point of view, we prove that the nonmaximality of an equilibrium ? is equivalent to its linear instability in the original dynamics, and to the linear instability of the disease-free state in the modified dynamics where we vaccinate according to ?. |
Impact of Opinion Formation Phenomena in Epidemic Dynamics: Kinetic Modeling on Networks
| Pengarang | : | Giacomo Albi, Elisa Calzola, Giacomo Dimarco, Mattia Zanella |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 779-805 |
| Abstrak | : | After the recent COVID-19 outbreaks, it became increasingly evident that individuals’ thoughts and beliefs can have a strong impact on disease transmission. It becomes therefore important to understand how information and opinions on protective measures evolve during epidemics. To this end, incorporating the impact of social media is essential to take into account the hierarchical structure of these platforms. In this context, we present a novel approach to take into account the interplay between infectious disease dynamics and socially structured opinion dynamics. Our work extends a conventional compartmental framework including behavioral attitudes in shaping public opinion and promoting the adoption of protective measures under the influence of different degrees of connectivity. The proposed approach is able to reproduce the emergence of epidemic waves. Specifically, it provides a clear link between the social influence of highly connected individuals and the epidemic dynamics. Through a heterogeneity of numerical tests we show how this comprehensive framework offers a more nuanced understanding of epidemic dynamics in the context of modern information dissemination and social behavior. |
A High-Order Perturbation of Envelopes (HOPE) Method for Vector Electromagnetic Scattering by Periodic Inhomogeneous Media: Joint Analyticity
| Pengarang | : | David P. Nicholls, Liet Vo |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 755-778 |
| Abstrak | : | The scattering of electromagnetic waves by three-dimensional periodic structures is important for many problems of crucial scientific and engineering interest. Due to the complexity and three-dimensional nature of these waves, fast, accurate, and reliable numerical simulation of these are indispensable for engineers and scientists alike. For this, high-order spectral methods are frequently employed and here we describe an algorithm in this class. Our approach is perturbative in nature where we view the deviation of the permittivity from a constant value as the deformation and we pursue regular perturbation theory. More specifically, we expand the three-dimensional, vector-valued electric field in a Taylor series in this small deformation parameter, derive recursions that each term in this series must satisfy, invoke a novel elliptic theory to establish bounds on the size of each correction, and thereby show that the purported Taylor series does, in fact, converge. Beyond this, we show that each of these terms in the Taylor series is jointly analytic in all three spatial variables by estimating solutions of governing equations for derivatives of these terms. This work extends our previous contribution regarding the Helmholtz equation to the full vector Maxwell equations, by providing a rigorous analyticity theory, both in deformation size and spatial variable (provided that the permittivity is, itself, analytic). |
Optimal Strategy for Trail Running with Nutrition and Fatigue Factors
| Pengarang | : | Bogna Jaszczak, ?ukasz P?ociniczak |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 730-754 |
| Abstrak | : | This paper presents an extension of Keller’s classical model to address the dynamics of long-distance trail running, a sport characterized by varying terrains, changing elevations, and the critical influence of in-race nutrition uptake. The optimization of the generalized Keller’s model is achieved through rigorous application of optimal control theory, specifically the Pontryagin maximum principle. This theoretical framework allows us to derive optimal control strategies that enhance the runner’s performance, taking into account the constraints imposed by the changing terrain, nutritional dynamics, and the evolving fatigue factor. To validate the practical applicability of the model, simulations are performed using real-world data obtained from various mountain races. The scenarios cover various trail conditions and elevation profiles. The performance of the model is systematically evaluated against these scenarios, demonstrating its ability to capture the complexities inherent in long-distance trail running and providing valuable insight into optimal race strategies. The error in the total race-time prediction is on the order of several percent, which may give the runner a reliable tool for choosing an optimal strategy before the actual race. |
On a Reaction-Diffusion-Advection Glucose Metabolism Model
| Pengarang | : | Yiwen Tao, Junping Shi |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 711-729 |
| Abstrak | : | A reaction-diffusion-advection glucose metabolism model is proposed to describe the spatiotemporal behaviors of glucose in the pancreatic islet. The global existence and boundedness of the solution to the model are proved, and the existence and uniqueness of the positive steady state are established. Spatiotemporal sensitivity index and correlation index are proposed to identify high-impact physiological factors and illustrate parameter interdependency. Additionally, different stages of glucose metabolism such as hyperinsulinemia, hypoglycemia, euglycemia, and diabetes are simulated to demonstrate the system’s dynamics under varying physiological conditions. These findings provide valuable guidance in the therapeutic process, aiding in the development of effective interventions. |
The Impact of Fear and Behavior Response to Established and Novel Diseases
| Pengarang | : | Avneet Kaur, Rebecca C. Tyson, Iain R. Moyles |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 687-710 |
| Abstrak | : | We analyze a disease transmission model that allows individuals to acquire fear and change their behavior to reduce transmission. Fear is acquired through contact with infected individuals and through the influence of fearful individuals. We analyze the model in two limits: First, an established disease limit (EDL), where the spread of the disease is much faster than the spread of fear, and second, a novel disease limit (NDL), where the spread of the disease is comparable to that of fear. For the EDL, we show that the relative rate of fear acquisition to disease transmission controls the size of the fearful population at the end of a disease outbreak, and that the fear-induced contact reduction behavior has very little impact on disease burden. Conversely, we show that in the NDL, disease burden can be controlled by fear-induced behavior depending on the rate of fear loss. Specifically, fear-induced behavior introduces a contact parameter ?, which if too large prevents the contact reduction from effectively managing the epidemic. We analytically identify a critical prophylactic behavior parameter ?=?? where this happens leading to a discontinuity in epidemic prevalence. We show that this change in disease burden introduces delayed epidemic waves. |
Bifurcation-Induced Species Coexistence in a Stage-Structured Intraguild Predation Model
| Pengarang | : | Wanxiao Xu, Hongying Shu, Lin Wang, Guihong Fan |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 662-686 |
| Abstrak | : | We incorporate a stage structure characterized by the maturation delay of intraguild (IG) prey into a three-species IG predation (IGP) model. We derive conditions for the existence and stability of nonnegative equilibria. By selecting the IG prey maturation delay as a bifurcation parameter at the positive equilibrium, we perform Hopf bifurcation analysis and obtain stability switch results. Furthermore, we conduct double Hopf bifurcation analysis using the mortality rate of immature IG prey and the maturation delay of IG prey as bifurcation parameters to further categorize the model dynamics near the double Hopf bifurcation points. It is demonstrated that our model exhibits complex dynamic behavior, such as stability switches, the coexistence of multiple stable periodic solutions, and quasi-periodic orbits. Our findings indicate that Hopf bifurcation and double Hopf bifurcation can lead to multiple types of species coexistence: Species coexist at the equilibrium or through sustained oscillations or irregular oscillations. |