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In this work, a new class of spectral conjugate gradient (CG) method is proposed for solving unconstrained optimization models. The search direction of the new method uses the ZPRP and JYJLL CG coefficients. The search direction satisfies the descent condition independent of the line search. The global convergence properties of the proposed method under the strong Wolfe line search are proved with some certain assumptions. Based on some test functions, numerical experiments are presented to show the proposed method's efficiency compared with other existing methods. The application of the proposed method for solving regression models of COVID-19 is provided. Mathematics subject classification: 65K10, 90C52, 90C26. Copyright © 2022 Novkaniza, Malik, Sulaiman and Aldila.
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In this article, we propose and analyze a mathematical model of COVID-19 transmission among a closed population, with social awareness and rapid test intervention as the control variables. For this, we have constructed the model using a compartmental system of the ordinary differential equations. Dynamical analysis regarding the existence and local stability of equilibrium points is conducted rigorously. Our analysis shows that COVID-19 will disappear from the population if the basic reproduction number is less than one, and persist if the basic reproduction number is greater than one. In addition, we have shown a trans-critical bifurcation phenomenon based on our proposed model when the basic reproduction number equals one. From the elasticity analysis, we have observed that rapid testing is more promising in reducing the basic reproduction number as compared to a media campaign to improve social awareness on COVID-19. Using the Pontryagin Maximum Principle (PMP), the characterization of our optimal control problem is derived analytically and solved numerically using the forward-backward iterative algorithm. Our cost-effectiveness analysis shows that using rapid test and media campaigns partially are the best intervention strategy to reduce the number of infected humans with the minimum cost of intervention. If the intervention is to be implemented as a single intervention, then using solely the rapid test is a more promising and low-cost option in reducing the number of infected individuals vis-a-vis a media campaign to increase social awareness as a single intervention. © 2021 Published by Indonesian Biomathematical Society,.
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Influenza is an infectious disease that can threaten the lives of people at high risk of complications. As vaccines are expected to strongly aid the prevention of diseases such as influenza and COVID-19, this research discusses how a modification of the well-known Susceptible-Vaccinated-Infected-Recovered-Susceptible (SVIRS) model can help prevent these diseases. This study involves employing a combination of vaccination and social distancing as a means of preventing these diseases. The SVIRS model divides the human population into four subpopulations:, those susceptible to influenza, vaccinated, infected, and recovered from influenza. Subpopulations of people who have been given the vaccine are also assumed to be susceptible to influenza, owing to the imperfect effectiveness of the vaccine. Also, since immunity to the disease is not life-long, there is a possibility that recovered individuals may get re-infected. Analytical studies of the nondimensionalization process and the existence and stability of the equilibrium points were carried out on the model, using the bifurcation analysis. Finally, a few numerical simulations were carried out using several scenarios of vaccination and social distancing strategies. Our model indicated the possibility of backward bifurcation at R0 = 1. Based on the analytical studies, R0 gave an insight to determine the best strategy that can be used to prevent the spread of influenza among the population. © 2021 Author(s).
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In this paper, a system of ordinary differential equation approach is developed to understand the spread of COVID-19. We first formulate the dynamic model by dividing the human population based on their health status, awareness status, and also including the free virus on the environment. We provide a basic analysis of the model regarding the well-posed properties and how the basic reproduction number can be used to determine the final state of COVID-19 in the population. A Pontryagin Maximum's Principle used to construct the model as an optimal control problem in a purpose to determine the most effective strategies against the spread of COVID-19. Three control strategies involved in the model, such as media campaign to develop an awareness of individuals, medical masks to prevent direct transmission, and use of disinfectant to reduce the number of free virus in the environment. Through numerical simulations, we find that the time-dependent control succeeds in reducing the outbreak of COVID-19. Furthermore, if the intervention should be implemented as a single intervention, then the media campaign gives the most effective cost strategy. © The Authors, published by EDP Sciences, 2020.
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A mathematical model for understanding the COVID-19 transmission mechanism proposed in this article considering two important factors: the path of transmission (direct-indirect) and human awareness. Mathematical model constructed using a four-dimensional ordinary differential equation. We find that the Covid-19 free state is locally asymptotically stable if the basic reproduction number is less than one, and unstable otherwise. Unique endemic states occur when the basic reproduction number is larger than one. From sensitivity analysis on the basic reproduction number, we find that the media campaign succeeds in suppressing the endemicity of COVID-19. Some numerical experiments conducted to show the dynamic of our model respect to the variation of parameters value. © The Authors, published by EDP Sciences, 2020.
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Since it was first discovered in Wuhan, China, COVID-19 has continued to spread throughout the world. Since then, many research works have been conducted to understand the spread of COVID-19. In this article, we propose an epidemiological model to understand the spread of COVID-19, considering the saturated treatment rate, direct/indirect transmission, and optimal control problem to find the best strategy for the COVID-19 eradication program. The model constructed is based on a nonlinear system of ordinary differential equations. Analytical results regarding the basic reproduction number and all equilibrium points are obtained analytically. Our model shows a possibility of the existence of the COVID-19 endemic state such that even the basic reproduction number is less than unity. We also found that indirect transmission contributes to the increases in the basic reproduction number and also the occurrence of the multiple endemic states. An optimal control approach was applied to determine the best strategy for the COVID-19 eradication program. Three control parameters were considered in the model: medical mask, disinfectant, and medical treatment. A Pontryagin’s Maximum Principle was used to derive the optimal control characterization of the related model and was solved numerically using the forward-backward iterative method. Several simulations were conducted to determine the impact of interventions for short time experiments. From the cost-effectiveness analysis, we found that using a medical mask as a single intervention is the most effective strategy to reduce the spread of infection. © SCIK Publishing Corporation. All rights reserved.