This study develops a reaction-diffusion model to investigate the transmission dynamics of brucellosis in a heterogeneous environment. We first establish the well-posedness of the system and derive the basic reproduction number R_0 . For the homogeneous case with heterogeneous diffusion, a complete global dynamical classification is established: the disease-free equilibrium is globally stable if R_0≤ 1 , while the endemic equilibrium is globally asymptotically stable if R_0 > 1 . Numerical simulations validate these theoretical results. Crucially, a global sensitivity analysis of R_0 identifies culling infected animals as the most effective single intervention for reducing transmission, outperforming vaccination and environmental disinfection. Based on this finding, we propose targeted control strategies, emphasizing that integrated measures—prioritizing early identification and culling of infected livestock—offer the most effective pathway for disease containment. This work provides both theoretical insights and practical guidance for optimizing brucellosis control.
This paper is concerned with the existence of a ground state solution for the following class of elliptic Kirchhoff-Boussinesq type problems given by Δ ^2 u ±Δ _p u + V(x)u= f(u) +γ |u|^2_**-2u in ℝ^N, where 2< p≤ 2^*= 2N/N-2 for N≥ 5 and 2_**= 2N/N-4 . The potential V can change sign and f is a continuous function with subcritical growth and behaves like |u|^q-2u with p< q< 2_** . We show the existence of a ground state solution using variational methods, Splitting Lemma and considering the subcritical case, i.e, γ =0 and the critical case, i.e, γ =1 .
The Riemann problem for the varying Chaplygin gas Euler equations with zeroth-order terms is investigated. By the varying Chaplygin gas, we mean that the fluid obeys the pressure-density-time relation where the pressure is negative and is the product of a function of time and the inverse of the density. It includes the Chaplygin gas as an exceptional case. Through the variable substitution method, the solution formed by two contact discontinuities and the solution with delta-shock are constructed in completely explicit forms. Under the generalized Rankine-Hugoniot relation and entropy condition, the position, propagation speed and strength of the delta-shock are uniquely determined. It is discovered that the shape of delta-shock in characteristic plane is either an exponential type curve or a straight line. An interesting phenomenon concerning the delta-shock is that even when the delta-shock is a straight line, its weight is no longer linear function of time. The phenomenon is attributed to the presence of the mass source term. It means that mass source term can play a role in adjusting the weight of the delta-shock. Additionally, it is proved that the constructed Riemann solutions tend to those of nonhomogeneous zero-pressure Euler equations with the same initial data as varying Chaplygin gas tends to zero, and the constructed Riemann solutions converge to the corresponding ones of Chaplygin gas Euler equations with same initial data as both source terms vanish simultaneously.
We consider the Eulerian droplet model with a varying generalized Chaplygin gas, which possesses negative pressure and is a product of a function of time and the inverse of a power of the density. The non-self-similar Riemann solutions are obtained, and then the limiting behavior of the Riemann solutions is investigated. As the parameter decreases to a critical value, the two-shock solution converges to a delta shock wave of the same system. Further, when the parameter goes to zero(vanishing pressure), the solution becomes exactly the delta shock wave solution of the zero-pressure Eulerian droplet model. Moreover, the two-rarefaction wave solution tends to a solution consisting of four contact discontinuities together with vacuum states, which is different from the vacuum solution of the zero-pressure Eulerian droplet model. The solution containing one rarefaction wave and one shock wave tends to the contact discontinuity solution of the zero-pressure Eulerian droplet model as pressure vanishes.
This work focuses on Nicholson’s blowflies model with mixed time-varying delays, a non-linear Immigration term, and (ς _1,ς _2) -pseudo-compact almost-automorphic parameters. The main contribution consists of improving and generalizing some existing results about (ς _1,ς _2) -pseudo compact almost-automorphic functions. Then, based on differential inequalities, the fixed point theorem, and the Halanay inequality, we establish some sufficient conditions for the existence, stability, and attractivity of positive solutions for the model considered. Further, we present a numerical example to support and illustrate the theoretical findings. Finally, a conclusion is drawn. Our findings are new and extend some existing results in the literature.
