Containing Misinformation Spread: A Collaborative Resource Allocation Strategy for Knowledge Popularization and Expert Education

With the prevalence of online social networks, the potential threat of misinformation has greatly enhanced. Therefore, it is significant to study how to effectively control the spread of misinformation. Publishing the truth to the public is the most effective approach to controlling the spread of misinformation. Knowledge popularization and expert education are two complementary ways to achieve that. It has been proven that if these two ways can be combined to speed up the release of the truth, the impact caused by the spread of misinformation will be dramatically reduced. However, how to reasonably allocate resources to these two ways so as to achieve a better result at a lower cost is still an open challenge. This paper provides a theoretical guidance for designing an effective collaborative resource allocation strategy. First, a novel individual-level misinformation spread model is proposed. It well characterizes the collaborative effect of the two truth-publishing ways on the containment of misinformation spread. On this basis, the expected cost of an arbitrary collaborative strategy is evaluated. Second, an optimal control problem is formulated to find effective strategies, with the expected cost as the performance index function and with the misinformation spread model as the constraint. Third, in order to solve the optimal control problem, an optimality system that specifies the necessary conditions of an optimal solution is derived. By solving the optimality system, a candidate optimal solution can be obtained. Finally, the effectiveness of the obtained candidate optimal solution is verified by a series of numerical experiments.

Optimal control application to the epidemiology of HBV and HCV co-infection

It is very important to note that a mathematical model plays a key role in different infectious diseases. Here, we study the dynamical behaviors of both hepatitis B virus (HBV) and hepatitis C virus (HCV) with their co-infection. Actually, the purpose of this work is to show how the bi-therapy is effective and include an inhibitor for HCV infection with some treatments, which are frequently used against HBV. Local stability, global stability and its prevention from the community are studied. Mathematical models and optimality system of nonlinear DE are solved numerically by RK4. We use linearization, Lyapunov function and Pontryagin’s maximum principle for local stability, global stability and optimal control, respectively. Stability curves and basic reproductive number are plotted with and without control versus different values of parameters. This study shows that the infection will spread without control and can cover with treatment. The intensity of HBV/HCV co-infection is studied before and after optimal treatment. This represents a short drop after treatment. First, we formulate the model then find its equilibrium points for both. The models possess four distinct equilibria: HBV and HCV free, and endemic. For the proposed problem dynamics, we show the local as well as the global stability of the HBV and HCV. With the help of optimal control theory, we increase uninfected individuals and decrease the infected individuals. Three time-dependent variables are also used, namely, vaccination, treatment and isolation. Finally, optimal control is classified into optimality system, which we can solve with Runge–Kutta-order four method for different values of parameters. Finally, we will conclude the results for implementation to minimize the infected individuals.

Crank-Nicolson finite difference schemes for parabolic optimal Dirichlet boundary control problem

In this paper, we adopt the optimize-then-discretize approach to solve parabolic optimal Dirichlet boundary control problem. First, we derive the first-order necessary optimality system, which includes the state, co-state equations and the optimality condition. Then, we propose Crank-Nicolson finite difference schemes to discretize the optimality system in 1D and 2D cases, respectively. In order to build the second order spatial approximation, we use the ghost points on the boundary in the schemes. We prove that the proposed schemes are unconditionally stable, compatible and second-order convergent in both time and space. To avoid solving the large coupled schemes directly, we use the iterative method. Finally, we present a numerical example to validate our theoretical analysis.

Optimal cloud assistance policy of end-edge-cloud ecosystem for mitigating edge distributed denial of service attacks

Edge computing has become a fundamental technology for Internet of Things (IoT) applications. To provide reliable services for latency-sensitive applications, edge servers must respond to end devices within the shortest amount of time possible. Edge distributed denial-of-service (DDoS) attacks, which render edge servers unusable by legitimate IoT applications by sending heavy requests from distributed attacking sources, is a threat that leads to severe latency. To protect edge servers from DDoS attacks, a hybrid computing paradigm known as an end-edge-cloud ecosystem provides a possible solution. Cloud assistance is allowed with this architecture. Edge servers can upload their pending tasks onto a cloud center for a workload reduction when encountering a DDoS attack, similar to borrowing resources from the cloud. Nevertheless, before using the ecosystem to mitigate edge DDoS attacks, we must address the core problem that edge servers must decide when and to what extent they should upload tasks to the cloud center. In this study, we focus on the design of optimal cloud assistance policies. First, we propose an edge workload evolution model that describes how the workload of the edge servers change over time with a given cloud assistance policy. On this basis, we quantify the effectiveness of the policy by using the resulting overall latency and formulate an optimal control problem for seeking optimal policies that can minimize such latency. We then provide solutions by deriving the optimality system and discuss some properties of the optimal solutions to accelerate the problem solving. Next, we introduce a numerical iterative algorithm to seek solutions that can satisfy the optimality system. Finally, we provide several illustrative numerical examples. The results show that the optimal policies obtained can effectively mitigate edge DDoS attacks.

The COVID-19 Model with Partially Recovered Carriers

Novel coronavirus (COVID-19) has been spreading and wreaking havoc globally, despite massive efforts by the government and World Health Organization (WHO). Consideration of partially recovered carriers is hypothesized to play a leading role in the persistence of the disease and its introduction to new areas. A model for transmission of COVID-19 by symptomless partially recovered carriers is proposed and analysed. It is shown that key parameters can be identified such that below a threshold level, built on these parameters, the epidemic tends towards extinction, while above another threshold, it tends towards a nontrivial epidemic state. Moreover, optimal control analysis of the model, using Pontryagin’s maximum principle, is performed. The optimal controls are characterized in terms of the optimality system and solved numerically for several scenarios. Numerical simulations and sensitivity analysis of the basic reproduction number, R c , indicate that the disease is mainly driven by parameters involving the partially recovered carriers rather than symptomatic ones. Moreover, optimal control analysis of the model, using Pontryagin’s maximum principle, is performed. The optimal controls were characterized in terms of the optimality system and solved numerically for several scenarios. Numerical simulations were explored to illustrate our theoretical findings, scenarios were built, and the model predicted that social distancing and treatment of the symptomatic will slow down the epidemic curve and reduce mortality of COVID-19 given that there is an average adherence to social distancing and effective treatment are administered.

Optimal Cloud Assistance Policy of End-Edge-Cloud Ecosystem for Mitigating Edge Distributed Denial of Service Attacks

Edge computing has become a fundamental technology for Internet of Things (IoT) applications. To provide reliable services for latency-sensitive applications, edge servers must respond to end devices within the shortest amount of time possible. Edge distributed denial-of-service (DDoS) attacks, which render edge servers unusable by legitimate IoT applications by sending heavy requests from distributed attacking sources, is a threat that leads to severe latency. To protect edge servers from DDoS attacks, a hybrid computing paradigm known as an end-edge-cloud ecosystem provides a possible solution. Cloud assistance is allowed with this architecture. Edge servers can upload their pending tasks onto a cloud center for a workload reduction when encountering a DDoS attack, similar to borrowing resources from the cloud. Nevertheless, before using the ecosystem to mitigate edge DDoS attacks, we must address the core problem that edge servers must decide when and to what extent they should upload tasks to the cloud center. In this study, we focus on the design of optimal cloud assistance policies. First, we propose an edge workload evolution model that describes how the workload of the edge servers change over time with a given cloud assistance policy. On this basis, we quantify the effectiveness of the policy by using the resulting overall latency and formulate an optimal control problem for seeking optimal policies that can minimize such latency. We then provide solutions by deriving the optimality system and discuss some properties of the optimal solutions to accelerate the problem solving. Next, we introduce a numerical iterative algorithm to seek solutions that can satisfy the optimality system. Finally, we provide several illustrative numerical examples. The results show that the optimal policies obtained can effectively mitigate edge DDoS attacks.

Optimal control of a chemotaxis equation arising in angiogenesis

<abstract><p>In this paper we consider an optimal control for an equation that models a crucial step in the tumor development, the angiogenesis. We show the existence of an optimal control, we characterize the optimal control as a solution of the optimality system and we show the uniqueness of the optimal control for short times.</p></abstract>

ON OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS FOR TYPHOID FEVER MODEL

Typhoid fever is a disease of a major concern in the developing world because it adversely affects on health and finance of a large chunk of people in this part of the world. This paper is aim to develop an extend and improve the optimal control model of typhoid transmission dynamics that can select the best cost-effective strategy for some interventions. Thus, an optimal control model for typhoid, incorporating control functions representing measures of personal hygiene and sanitation, diagnosis and treatment, and vaccination, was formulated. The corresponding optimality system was characterized via the Pontryagin’s maximum principle. The optimality system was numerically simulated for all possible strategies using Runge-Kutta method of order four. For cost-effectiveness analysis, the method of incremental cost-effectiveness ratio (ICER) was employed. The results show that the model is able to select the most cost-effective strategy for any given set of parameter values and initial conditions. Key words: Optimal control, Pontryagin’s maximum principle, cost-effectiveness

On the Optimal Control of Stationary Fluid–Structure Interaction Systems

Fluid–structure interaction (FSI) systems consist of a fluid which flows and deforms one or more solid surrounding structures. In this paper, we study inverse FSI problems, where the goal is to find the optimal value of some control parameters, such that the FSI solution is close to a desired one. Optimal control problems are formulated with Lagrange multipliers and adjoint variables formalism. In order to recover the symmetry of the stationary state-adjoint system an auxiliary displacement field is introduced and used to extend the velocity field from the fluid into the structure domain. As a consequence, the adjoint interface forces are balanced automatically. We present three different FSI optimal controls: inverse parameter estimation, boundary control and distributed control. The optimality system is derived from the first order necessary condition by taking the Fréchet derivatives of the augmented Lagrangian with respect to all the variables involved. The optimal solution is obtained through a gradient-based algorithm applied to the optimality system. In order to support the proposed approach and compare these three optimal control approaches numerical tests are performed.