Cancer diseases lead to the second-highest death rate all over the world. For treating tumors, one of the most common schemes is chemotherapy, which can decrease the tumor size and control the progression of cancer diseases. To better understand the mechanisms of chemotherapy, we developed a mathematical model of tumor growth under chemotherapy. This model includes both immune system response and drug therapy. We characterize the symmetrical properties and dynamics of this differential equation model by finding the equilibrium points and exploring the stability and symmetry properties in a range of model parameters. Sensitivity analyses suggest that the chemotherapy drug-induced tumor mortality rate and the drug decay rate contribute significantly to the determination of treatment outcomes. Numerical simulations highlight the importance of CTL activation in tumor chemotherapy.

This paper investigates the combined damped sinusoidal oscillation solutions to the 3 + 1 -D variable-coefficient (VC) generalized nonlinear wave equation. The bilinear form is considered in terms of Hirota derivatives. Accordingly, we utilize a binary Bell polynomial transformation for reducing the Cole-Hopf algorithm to get the exact solutions of the VC generalized NLW equation. The damped sinusoidal oscillations for two cases of the nonlinear wave ordinary differential equation will be studied. Using suitable mathematical assumptions, the novel kinds of solitary, periodic, and singular soliton solutions are derived and established in view of the trigonometric and rational functions of the governing equation. To achieve this, the illustrative example of the VC generalized nonlinear wave equation is provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of the free parameters on the behavior of acquired figures of a few obtained solutions for two nonlinear rational exact cases was also discussed. By comparing the proposed method with the other existing methods, the results show that the execution of this method is concise, simple, and straightforward.

<abstract><p>In this study, we investigated the threshold dynamics of a spatially heterogeneous nonlocal diffusion West Nile virus model. By employing semigroup theory and continuous Fréchet-differentiable, we established the well-posedness of the solution. The expression for the basic reproduction number derived using the next-generation matrix method. The authors demonstrated the threshold dynamics of the system by constructing a Lyapunov function and applying the comparison principle. Finally, numerical simulations were used to validate the theorem results. It can be suggested that to control disease development rapidly, measures should be taken to reduce the spread of mosquitoes and birds.</p></abstract>

Brucellosis is a major worldwide problem in public health. In this paper, we established and analyzed the Susceptible-Exposed-Infectious-Vaccinated for small ruminant–Susceptible-Exposed-Infectious-Vaccinated for cattle–Susceptible-Infectious-Recovered for human (SEIV–SEIV–SIR) model of Brucellosis with an incubation period which considered that human was infected through direct contact with infected humans, infected small ruminant, infected cattle and indirect contact with Brucella in the environment. The basic reproduction number [Formula: see text] of the model is computed by the spectral radius of the next-generation matrix. We proved that the disease-free equilibrium exists and we analyzed that the disease-free equilibrium point and endemic equilibrium point are global stability by constructing the [Formula: see text] function and applying the [Formula: see text] invariant principle. Numerical solutions and analytical reveal that the prevention and control measures for Brucella should be to detect infected livestock in time, reduce contact with infected livestock and increase the cure rate of infected humans.

The significance of information management is getting more and more prominent in the knowledge-based economy age. The problems in construction and development of information management specialty in regional colleges and universities are discussed and the countermeasures for development are put forward so that is a virtuous development (Abstract)