Model Dinamika Penyebaran Dbd Dengan Menerapkan Tiga Strategi Pengendaliannya

The information of the dynamic of dengue fever is needed to build the model of its controlling strategy. Therefore, this research is aimed to develop a mathematical model such that the effectiveness of several controlling strategy for example 3M campaign, treatment to the infected people, andthe applying ofinsecticide can be evaluated. This mathematical model is constructed by classifying the human population into three class that are Suspectible (S), Infected (I) and Removed (R) while the vector population (aedes aegypti mosquito) is assumed belongs to the Infected (I) class. The effectiveness of the controlling strategy is analyzed using maximum Pontryagin principle. The result of this analysis shows that the 3M campaign affects the size of the suspect population

Analysis, Simulation and Control of a New Measles Epidemic Model

In this paper the problem of modeling and controlling the measles epidemic spread is faced. A new model is proposed and analysed; besides the categories usually considered in measles modeling, the susceptible, the exposed, the infected, the removed and, less frequently, the quarantine individuals, two new categories are herein introduced: the immunosuppressed subjects, that can not be vaccinated, and the patients with an additional complication, not risky by itself but dangerous if caught togeter with the measles. These two novelties are taken into account in designing and scheduling suitably control actions such as vaccination, whenever possible, prevention, quarantine and treatment, when limited resources are available. An analysis of the model is developed and the optimal control strategies are compared with other not optimized actions. By using the Pontryagin principle, it is shown the prevailing role of the vaccination in guaranteeing the protection to immunosuppressed individuals, as well as the importance of a prompt response of the society when an epidemic spread occurs, such as the quarantine intervention

An Improvement in a Local Observer Design for Optimal State Feedback Control: The Case Study of HIV/AIDS Diffusion

The paper addresses the problem of an observer design for a nonlinear system for which a preliminary linear state feedback is designed but the full state is not measurable. Since a linear control assures the fulfilment of local approximated conditions, usually a linear observer is designed in these cases to estimate the state with estimation error locally convergent to zero. The case in which the control contains an external reference, like in regulations problems, is studied, showing that the solution obtained working with the linear approximation to get local solutions produces non consistent results in terms of local regions of convergence for the system and for the observer. A solution to this problem is provided, proposing a different choice for the observer design which allows to obtain all conditions locally satisfied on the same local region in the neighbourhood of a new equilibrium point. The case study of an epidemic spread control is used to show the effectiveness of the procedure. The linear control with regulation term is present in this case because the problem is reconducted to a Linear Quadratic Regulation problem. Simulation results show the differences between the two approaches and the effectiveness of the proposed on

Bifurcation analysis and optimal control of a network-based SIR model with the impact of medical resources

A new network-based SIR epidemic model, which incorporates the individual medical resource factor and public medical resource factor is proposed. It is verified that the larger the public medical resource factor, the smaller the control reproduction number, and the larger individual medical resource factor can weaken the spread of diseases. We found that the control reproduction number below unity is not enough to ensure global asymptotic stability of the disease-free equilibrium. When the number of hospital beds or the individual medical resource factor is small enough, the system will undergoes backward bifurcation. Moreover, the existence and uniqueness of the optimal control and two time-varying variables’s optimal solutions are obtained. On the scale-free network, the level of optimal control is also proved to be different for different degrees. Finally, the theoretical results are illustrated by numerical simulations. This study suggests that maintaining sufficient both public medical resources and individual medical resources is crucial for the control of infectious diseases

Early estimation of the number of hidden HIV infected subjects: An extended Kalman filter approach

In the last decades several epidemic emergencies have been affecting the world, influ encing the social relationships, the economics and the habits. In particular, starting in the early 0 80, the Acquired Immunodeficiency Syndrome, AIDS, is representing one of the most worrying sanitary emergency, that has caused up to now more than 25 million of dead patients. The infection is caused by the Human Immunodeficiency Virus, HIV, that may be transmitted by body fluids; therefore with wise behaviours the epidemic spread could rapidly be contained. This sanitary emergency is peculiar for the long incubation time: it can reach even 10 years, a long period in which the individual can unconsciously infect other subjects. The identification of the number of infected unaware people, mandatory to define suitable containment measures, is here obtained by using the extended Kalman filter applied to a noisy model in which, reasonably, only the number of infected diagnosed patients is available. Numerical simulations and real data analysis support the effective ness of the approac

Reliable optimal controls for SEIR models in epidemiology

We present and compare two different optimal control approaches applied to SEIR models in epidemiology, which allow us to obtain some policies for controlling the spread of an epidemic. The first approach uses Dynamic Programming to characterise the value function of the problem as the solution of a partial differential equation, the Hamilton-Jacobi-Bellman equation, and derive the optimal policy in feedback form. The second is based on Pontryagin's maximum principle and directly gives open-loop controls, via the solution of an optimality system of ordinary differential equations. This method, however, may not converge to the optimal solution. We propose a combination of the two methods in order to obtain high-quality and reliable solutions. Several simulations are presented and discussed

Beyond just “flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions

When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple “flattening of the curve”. Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany. © 2020, The Author(s)

Beyond just ``flattening the curve'': Optimal control of epidemics with purely non-pharmaceutical interventions

When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple "flattening of the curve". Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany

Mathematical Modeling of Transmission Dynamics and Optimal Control of Vaccination and Treatment for Hepatitis B Virus

Hepatitis B virus (HBV) infection is a worldwide public health problem. In this paper, we study the dynamics of hepatitis B virus (HBV) infection which can be controlled by vaccination as well as treatment. Initially we consider constant controls for both vaccination and treatment. In the constant controls case, by determining the basic reproduction number, we study the existence and stability of the disease-free and endemic steady-state solutions of the model. Next, we take the controls as time and formulate the appropriate optimal control problem and obtain the optimal control strategy to minimize both the number of infectious humans and the associated costs. Finally at the end numerical simulation results show that optimal combination of vaccination and treatment is the most effective way to control hepatitis B virus infection