The mechanisms governing the transmission of most infectious diseases are by now well established within epidemiological theory. In order to provide a quantitative mathematical description of epidemic propagation, a wide range of compartmental models—including the SIR, SIS, SEIR, and SIRS formulations have been introduced and systematically analyzed. This work is devoted to the study of an initial value problem for a class of semilinear parabolic partial differential equations that arise in epidemic modeling with a general semilinear incidence function. The problem is formulated in a Hilbert space framework associated with a self-adjoint, positive definite operator. For the numerical approximation of solutions, we propose a high-order finite difference scheme. A rigorous analysis is carried out to prove the existence and uniqueness of bounded solutions for the resulting discrete system, with estimates that are uniform with respect to the time step. The analytical findings are illustrated through representative applications, where bounded solutions of the continuous model and their numerical counterparts are examined.
This paper investigates the existence and stability of periodic solutions for a generalized hematopoietic model on time scales with mixed delays, nonlinear harvesting, and impulsive perturbations. The model unifies continuous and discrete dynamics, providing a more realistic framework for clinical hematopoiesis. By applying the Leggett-Williams fixed point theorem, we derive sufficient conditions for the existence of multiple nonnegative periodic solutions under different parameter regimes. The Krasnoselskii fixed point theorem on cones is employed to establish the existence of at least one positive periodic solution. Furthermore, using the Banach contraction principle combined with Lyapunov functional techniques, we obtain criteria for the global exponential stability of the unique periodic solution, a result that has received limited attention in previous studies on hematopoietic models. Numerical simulations are provided to illustrate the effectiveness and applicability of the theoretical results.
This paper is a starting point in the systematic study of anisotropic partial sums of multiple Fourier series. The main result is an extension of one general estimate of the Lebesgue constants due to V. Yudin. The sharpness of the result obtained is also discussed.
Let p_t,-2(n) denote the number of 2-color overpartition pairs of n in which one of the colors appears only in parts that are multiples of t. In this article, we study divisibility properties of p_p^α ,-2(n) by arbitrary powers of 2 for all prime p. We also prove arithmetic properties of congruences satisfied by p_t,-2(n) for certain values of t using theta function identities, Hecke operators and the theory of modular forms.
Using the Steklov function, we prove an equivalence theorem between the K-functional and the modulus of smoothness associated with the Sobolev space in L^2(ℝ) . We also establish generalizations of the classical theorems of Bernstein and Jackson. To this end, we make use of functions with bounded spectrum.
