Dengue fever is a major public health problem and has been extensively modeled. Understanding the role of explicit vector dynamics in vector-borne diseases such as dengue fever is essential for accurately capturing transmission patterns and improving control strategies. In this study, we extend the minimalistic two-infection host-host SIRSIR model by introducing the SIRSIR-UV model, which explicitly incorporates vector population dynamics. Our aim is to investigate how these explicit vector dynamics influence the behavior of the system. In doing so, we extend previous models that assumed implicit vector effects in addition to immunity and disease enhancement factors. Using tools from nonlinear dynamics and bifurcation theory, we derive analytical conditions for transcritical and tangent bifurcations, formalize backward bifurcation using center manifold theory, and compute Hopf and global homoclinic bifurcation curves. We also show that seasonal influences in the vector populations, mimicking the seasonality of mosquitoes, contribute to the occurrence of chaotic behavior in disease transmission, reflecting the current patterns observed in epidemiological data. We thoroughly characterize the dynamics of the SIRSIR-UV model and explore the implications of including explicit vector dynamics. Finally, we discuss our results with the previous SIRSIR model and conclude that the bifurcation structures observed in the SIRSIR-UV model are consistent with those of the minimalistic SIRSIR model. This unexpected result has important implications for the modeling of vector-borne diseases. It suggests that simplifying assumptions, such as the use of implicit vector dynamics, can effectively capture important aspects of disease transmission while reducing the complexity of the mathematical analysis.
This paper explores the physics of magnetic and electric flux tubes supported by current vortices in condensed matter having a superconducting state in which bosonic charge carriers flow without resistance. The starting point is that the boson wave function satisfies the Klein–Gordon equation of relativistic quantum mechanics. Next, the electromagnetic fields within the superconducting medium are assumed to obey the quasistatic Maxwell equations expressed with geometric algebra and calculus and incorporating either electric or hypothetical magnetic currents. Finally, the Fundamental Theorem of Calculus is utilized in two forms to examine flux tubes, first in electric superconductors and then in hypothetical magnetic superconductors. Geometric algebra and calculus enable a consistent treatment of both analyses and an extension from three to four spatial dimensions.
This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that these Lie groups can be equivalently defined using norm functions of multivectors applied in the theory of spin groups. We also study the corresponding Lie algebras. Some of these Lie groups and algebras are closely related to Heisenberg Lie groups and algebras. The introduced groups are interesting for various applications in physics and computer science, in particular, for constructing equivariant neural networks.
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：