In this study, a nonlinear deterministic model for the transmission dynamics of skin sores (impetigo) disease is developed and analyzed by the help of stability of differential equations. Some basic properties of the model including existence and positivity as well as boundedness of the solutions of the model are investigated. The disease-free and endemic equilibrium were investigated, as well as the basic reproduction number, R0, also calculated using the next-generation matrix approach. When R0 < 1, the model's stability analysis reveals that the system is asymptotically stable at disease-free critical point globally as well as locally. If R0 > 1, the system is asymptotically stable at disease-endemic equilibrium both locally and globally. The long-term behavior of the skin sores model's steady state solution in a population is investigated using numerical simulations of the model.

In this article, a nonlinear mathematical model is constructed to investigate the conservation of depleted forest resources due to the increase of population and associated pressures. Fundamental equations governing the dynamics of the system are defined by the set of highly nonlinear ordinary differential equations and solved numerically. The model is analyzed by using the nature of stability analysis theory of dynamical system. The numerical solutions and simulations of the system are carried out using ODE45 subroutine of MATLAB. Presentations of results are revealed using graphs and interpreted biologically. It is noted that the increase of population density and associated pressures causes the depletion of forestry resources. However, forest resources can be conserved by controlling man made fire, toxicant activities, applying economical incentives and technological efforts. Recommendations for Resource managers The forest resources are natural resources that can be used for ecosystem balancing mechanism in nature. However, forest resources are depleted as a result of augmented population and associated pressures. Therefore, When population and associated pressures increase, the depletion of forestry resources increases. As conservation efforts applied, the density of forestry resources increases.

In this study, I developed a nonlinear mathematical model to explore the dynamics of citizens on electoral lists, as well as the impact of abstainers and voter registration on political electors. The models are analyzed for positive and boundedness, asymptotically stability of abstention-free and abstaining equilibrium points both locally and globally, and sensitivity analysis of model parameters based on the fundamental reproduction number R0. Finally, numerical simulations were carried out using the ODE45 subroutine of MATLAB to interpret using graphs. The findings demonstrate that abstainers have a detrimental impact on voter turnout. Now, is the time to raise voter awareness to educate them about the value of electoral and political involvement, protect them from the harmful effects of abstainers, and reduce the number of those who have registered but have not voted.

After breast cancer, cervical cancer is the second most frequent cancer in women globally. The Human Papillomavirus is the most common cause of cervical cancer. In this paper, we used a nonlinear ordinary differential equation system to build a mathematical model of cervical cancer with six compartments (the number of susceptible women, vaccinations of susceptible women, the infected women with HPV, the number of infected with cervical cancer, treatment individual, and recovery class). The model is examined using the existence of bounded and positive solutions, numerical analysis, sensitivity analysis, and stability analysis of disease-free and endemic equilibrium points as a function of R0 values. The numerical simulations of the system are carried out using the ODE45 subroutine of MATLAB and the results are revealed using graphs and biologically interpreted. Using numerical simulation, applying vaccination and increasing treatment for everyone can help to reduce and control the spread of cervical cancer.

This paper explores the impact of chemical reaction and thermal radiation on time-dependent hydromagnetic thin-film flow of a second-grade fluid across an inclined flat plate embedded in a porous medium. The thermal radiation based on the Rosseland approximation is incorporated in the energy equation. Uniform applied magnetic field and first-order homogenous chemical reaction are included in the momentum and concentration equations, respectively. The novel mathematical flow model is constructed by using a set of partial differential equations (PDEs). The PDEs are then transformed into an equivalent set of ordinary differential equations (ODEs) and solved by applying the Laplace transform method. However, the time domain solutions are obtained by using the INVLAP subroutine of MATLAB. Physical parameters influencing thin-film velocity, temperature, and concentration are illustrated graphically, while those affecting skin friction, heat, and mass transfer rates are presented in a tabular form. It is found that thin-film velocity and temperature boost with increasing values of thermal radiation, but thin-film velocity decreases with increasing values of chemical reaction and magnetic field. The current investigation is to enhance heat and mass transfer in the design of mechanical systems involving the thin film flow of second-grade fluids over an inclined flat plate after applying thermal radiation and chemical reaction.