A New Numerical Method to Solve Some in the Unit Ball and Comparison with the Finite Element and the Exact SolutionRead the full article
International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.
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Modelling the Control of the Impact of Fall Armyworm (Spodoptera frugiperda) Infestations on Maize Production
In this paper, we propose and analyze a stage-structured mathematical model for modelling the control of the impact of Fall Armyworm infestations on maize production. Preliminary analysis of the model in the vegetative and reproductive stages revealed that the two systems had a unique and positively bounded solution for all time . Numerical analysis of the model in both stages under two different cases was also considered: Case 1: different number of the adult moths in the field assumed at and Case 2: the existence of exogenous factors that lead to the immigration of adult moths in the field at time . The results indicate that the destruction of maize biomass which is accompanied by a decrease in maize plants to an average of 160 and 142 in the vegetative and reproductive stages, respectively, was observed to be higher in Case 2 than in Case 1 due to subsequent increase in egg production and density of the caterpillars in first few (10) days after immigration. This severe effect on maize plants caused by the unprecedented number of the pests influenced the extension of the model in both stages to include controls such as pesticides and harvesting. The results further show that the pest was significantly suppressed, resulting in an increase in maize plants to an average of 467 and 443 in vegetative and reproductive stages, respectively.
About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal Delays
This paper studies and investigates total stability results of a class of dynamic systems within a prescribed closed ball of the state space around the origin. The class of systems under study includes unstructured nonlinearities subject to multiple higher-order Lipschitz-type conditions which influence the dynamics and which can be eventually interpreted as unstructured perturbations. The results are also extended to the case of presence of multiple internal (i.e., in the state) point discrete delays. Some stability extensions are also discussed for the case when the systems are subject to forcing efforts by using links between the controllability and stabilizability concepts from control theory and the existence of stabilizing linear controls. The results are based on the ad hoc use of Gronwall’s inequality.
Modeling the Effect of External Computers and Removable Devices on a Computer Network with Heterogeneous Immunity
This paper intends to investigate the impact of external computers and removable devices on virus spread in a network with heterogeneous immunity. For that purpose, a new dynamical model is presented and discussed. Theoretical analysis reveals the existence of a unique viral equilibrium that is locally and globally asymptotically stable with no criteria. This result implies that efforts to eliminate viruses are not possible. Therefore, sensitivity analysis is performed to have more insight into parameters’ impact on virus prevalence. As a result, strategies are suggested to contain virus spread to an acceptable level. Finally, to rationalize the analytical results, we execute some numerical simulations.
Impact of Media-Induced Fear on the Control of COVID-19 Outbreak: A Mathematical Study
The COVID-19 pandemic has put the world in threat for a long time. It was first identified in Wuhan, China, in December 2019 and has been declared a pandemic by the WHO. This disease is mainly caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). So far, no vaccine or medicine has been developed for the proper treatment of this disease, so people are afraid of getting infected. The pandemic has placed many nations at the door of socioeconomic emergencies. Therefore, it is very important to predict the development trend of this epidemic, and we know mathematical modelling is a basic tool to research the dynamic behaviour of disease and predict the spreading trend of the disease. In this study, we have formulated a mathematical model for the COVID-19 outbreak by introducing a quarantine class with media-induced fear in the disease transmission rate to analyze the dynamic behaviour of this epidemic. We have calculated the basic reproduction number R0, and we observed that when R0 < 1, disease-free equilibrium is globally stable whereas if R0> 1, then the system is permanent and there exists a unique endemic equilibrium point. Global stability of the endemic equilibrium point is developed by using Li and Muldowney’s high-dimensional Bendixson criterion. Finally, some numerical simulations are performed using MATLAB to verify our analytical results.
Fuzzy Conformable Fractional Differential Equations
In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order .
Lie Symmetry Analysis and Explicit Solutions for the Time-Fractional Regularized Long-Wave Equation
This paper systematically investigates the Lie group analysis method of the time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions of the time-fractional (RLW) equation are obtained. It is shown that the governing equation can be transformed into a fractional ordinary differential equation with a new independent variable, where the fractional derivatives are in Erdèlyi–Kober sense. Furthermore, the explicit analytic solutions of the time-fractional (RLW) equation are obtained using the power series expansion method. Finally, some graphical features were presented to give a visual interpretation of the solutions.