Nonlinear Analysis: Modelling and Control
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Optimal control analysis of a malaria transmission model with applications to Democratic Republic of Congo
Full text linkIn this paper, a dynamical model of malaria transmission with vector-bias and timedependent controls is investigated. The controls include the RTS,S malaria vaccine, using insecticide-treated mosquito net, treatment of infectious human, and indoor spraying. For constant controls, the existence and stability of equilibrium, as well as the existence of backward bifurcation, are obtained. The sensitivity analysis quantifies the impact of parameters and controls on the basic reproduction number. For time-dependent controls, by using the Pontryagin’s maximum principle the existence and expression of optimal controls are established. As an application of the model and control strategies, the malaria transmission and controls in Democratic Republic of Congo are discussed. To be specific, we simulate the reported cases of Democratic Republic of Congo by World Health Organization and predict the trends. Cost-effectiveness analysis and numerical simulations show that combining all controls can minimize the number of infected humans to the full extent, using insecticide-treated mosquito net is the most cost-effectiveness strategy, combining RTS,S malaria vaccine with using insecticide-treated mosquito net and treatment of infectious human is also cost-effective among all the strategies with good effect
Existence and global asymptotic behavior of S-asymptotically periodic solutions for fractional evolution equation with delay
Full text linkThis paper discusses the S-asymptotically periodic problem of fractional evolution equation with delay. By introducing a new noncompact measure theory involving infinite interval, we study the existence of S-asymptotically periodic mild solutions under the situation that the relevant semigroup is noncompact and the nonlinear term satisfies more general growth conditions instead of Lipschitz-type conditions. Moreover, by establishing a new Gronwall-type integral inequality corresponding to fractional differential equation with delay, we consider the global asymptotic behavior of S-asymptotically periodic mild solutions, which will make up for the blank of this field
On the solvability of the Atangana–Baleanu fractional evolution equations: An integral contractor approach
Full text linkWe present existence and controllability results for mild solutions to the Atangana–Baleanu fractional evolution equations. We prove our results by applying bounded integral contractors and a sequencing technique. In contrast to the papers available in the literature, in order to establish our controllability results, we need not define the induced inverse of the controllability operator, and the pertinent nonlinear function need not necessarily satisfy a Lipschitz condition. In addition, we also establish trajectory controllability results. Finally, we discuss an application, which illustrates our results
A new conversation on the existence of Hilfer fractional stochastic Volterra–Fredholm integro-differential inclusions via almost sectorial operators
Full text linkThe existence of Hilfer fractional stochastic Volterra–Fredholm integro-differential inclusions via almost sectorial operators is the topic of our paper. The researchers used fractional calculus, stochastic analysis theory, and Bohnenblust–Karlin’s fixed point theorem for multivalued maps to support their findings. To begin with, we must establish the existence of a mild solution. In addition, to show the principle, an application is presented
An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operators
Full text linkIn this paper, we investigate the effect of hemivariational inequalities on the approximate controllability of Caputo fractional differential systems. The main results of this study are tested by using multivalued maps, sectorial operators of type (P, η, r, γ ), fractional calculus, and the fixed point theorem. Initially, we introduce the idea of mild solution for fractional hemivariational inequalities. Next, the approximate controllability results of semilinear control problems were then established. Moreover, we will move on to the system involving nonlocal conditions. Finally, an example is provided in support of the main results we acquired
Prešić-type fixed point results via Q-distance on quasimetric space and application to (p, q)-difference equations
Full text linkIn this paper, we introduce two new properties to the Q-function, called as the 0-property and the small self-distance property, which is frequently used in studies of fixed point theory in quasimetric spaces. Then, with the help of Q-functions having these properties, we present some fixed point theorems for Prešić-type mappings in quasimetric spaces. Finally, we state a theorem for the existence and uniqueness of the solution to a boundary value problem for (p, q)-difference equations to demonstrate the applicability of our theoretical results, which we support with an example
Fixed point theorems of new generalized C-conditions for (psi; gamma)-mappings in modular metric spaces and its applications
No full textThis paper introduces new generalizations of the C-condition for (ψ; γ)-mappings in modular metric spaces. We extend the fixed point results for such mappings yielding the generalized C-condition in metric spaces to modular ones.We proved the existence and uniqueness of solutions in modular metric spaces for these kinds of mappings. We give an example to emphasize that our results work in the difference between modularmetric spaces and usual ones. Moreover, we consider some initial and boundary value problems to support the results obtained here. We examine the existence and uniqueness of the solutions for the problems in modular metric spaces
Leader-following identical consensus for Markov jump nonlinear multi-agent systems subjected to attacks with impulse
Full text linkThe issue of leader-following identical consensus for nonlinear Markov jump multiagent systems (NMJMASs) under deception attacks (DAs) or denial-of-service (DoS) attacks is investigated in this paper. The Bernoulli random variable is introduced to describe whether the controller is injected with false data, that is, whether the systems are subjected to DAs. A connectivity recovery mechanism is constructed to maintain the connection among multi-agents when the systems are subjected to DoS attack. The impulsive control strategy is adopted to ensure that the systems can normally work under DAs or DoS attacks. Based on graph theory, Lyapunov stability theory, and impulsive theory, using the Lyapunov direct method and stochastic analysis method, the sufficient conditions of identical consensus for Markov jump multi-agent systems (MJMASs) under DAs or DoS are obtained, respectively. Finally, the correctness of the results and the effectiveness of the method are verified by two numerical examples
Global dynamics of a dengue fever model incorporating transmission seasonality
Full text linkThe changes of seasons cause that the transmission of dengue fever is characterized by periodicity. We develop a dengue fever transmission model incorporating seasonal periodicity and spatial heterogeneity. Based on the well-posedness of solution for this model, we propose its basic reproduction number R0, and we discuss the properties of this number including its limiting form when the diffusion coefficients change. Moreover, the dynamical behavior of this model infers that if R0 ⩽ 1, then the disease-free periodic solution is globally asymptotically stable, and if R0 > 1, then the model possesses a positive periodic solution, which is globally asymptotically stable. These theoretical findings are further illustrated by the final numerical simulations. Additionally, we add that the similar problem has been investigated by M. Zhu and Y. Xu [A time-periodic dengue fever model in a heterogeneous environment, Math. Comput. Simul., 155:115–129, 2019] in which some dynamical results have been studied only on the cases R0 < 1 and R0 > 1. Our results not only include the scenario on the case R0 = 1, but also involve the more succinct conditions on the cases R0 < 1 and R0 > 1
Steady-state bifurcation of FHN-type oscillator on a square domain
Full text linkThe Turing patterns of reaction-diffusion equations defined over a square region are more complex because of the D4-symmetry of the spatial region. This leads to the occurrence of multiple equivariant Turing bifurcations. In this paper, taking the FHN model as an example, we give a explicit calculation formula of normal form for the simple and double Turing bifurcation of the reaction-diffusion equation with Dirichlet boundary conditions and defined on a square space, and we also obtain a method for the calculation of the existence of spatially inhomogeneous steady-state solutions. This paper provides a theoretical basis for exploring and predicting the pattern formation of spatial multimode interaction