The effects of community interactions and quarantine on a complex network

Abstract: An adaptive complex network based on a susceptible-exposed-infectious-quarantine-recovered (SEIQR) framework is implemented to investigate the transmission dynamics of an infectious disease. The topology and its relations with network parameters are discussed. Using the primary outbreak data from the SEIQR network model, a regression model is developed to describe the relation between the quarantine rate and the key epidemiological parameters. We approximate the quarantine rate as a function of the number of individuals visiting communities and hubs, then incorporate it into the adaptive complex network to investigate the disease transmission dynamics. The proposed quantity can be estimated from the outbreak data and hence is more approachable as compared to the constant rate. Our results suggest that contact radius, hub radius, number of hubs, hub capacity and transmission rate may be important determinants to predict the disease spread and severity of outbreaks. Moreover, our results also suggest that during an outbreak, closing down certain public facilities or reducing their capacities and reducing the number of individuals visiting communities or public places, may significantly slow down the disease spread

The conditions for blow-up and global existence of solution for a degenerate and singular parabolic equation with a non-local source

In this paper, we consider the degenerate and singular porous medium equation with a non-local source  The conditions on the local and global existence of solutions are investigated. In the case of blow-up, the blow-up set is shown. Moreover, the uniform blow-up profile of the blow-up solution is given

A single quenching point for a fractional heat equation based on the Riemann-Liouville fractional derivative with a nonlinear concentrate source

Abstract This paper aims to study the quenching problem in a fractional heat equation with the Riemann-Liouville fractional derivative. The existence and uniqueness of a solution for the problem are obtained by transforming the problem to an equivalent integral equation. The condition for the quenching occurrence in a finite time is given. Furthermore, the quenching point set is shown

Laplace Transform Homotopy Perturbation Method for the Two Dimensional Black Scholes Model with European Call Option

The Black Scholes model is a well-known and useful mathematical model in financial markets. In this paper, the two-dimensional Black Scholes equation with European call option is studied. The explicit solution of this problem is carried out in the form of a Mellin–Ross function by using Laplace transform homotopy perturbation method. The solution example demonstrates that the proposed scheme is effective

Model Predictive Control of COVID-19 Pandemic with Social Isolation and Vaccination Policies in Thailand

This study concerns the COVID-19 pandemic in Thailand related to social isolation and vaccination policies. The behavior of disease spread is described by an epidemic model via a system of ordinary differential equations. The invariant region and equilibrium point of the model, as well as the basic reproduction number, are also examined. Moreover, the model is fitted to real data for the second wave and the third wave of the pandemic in Thailand by a sum square error method in order to forecast the future spread of infectious diseases at each time. Furthermore, the model predictive control technique with quadratic programming is used to investigate the schedule of preventive measures over a time horizon. As a result, firstly, the plan results are proposed to solve the limitation of ICU capacity and increase the survival rate of patients. Secondly, the plan to control the outbreak without vaccination shows a strict policy that is difficult to do practically. Finally, the vaccination plan significantly prevents disease transmission, since the populations who get the vaccination have immunity against the virus. Moreover, the outbreak is controlled in 28 weeks. The results of a measurement strategy for preventing the disease are examined and compared with a control and without a control. Thus, the schedule over a time horizon can be suitably used for controlling

An Analysis on the Fractional Asset Flow Differential Equations

The asset flow differential equation (AFDE) is the mathematical model that plays an essential role for planning to predict the financial behavior in the market. In this paper, we introduce the fractional asset flow differential equations (FAFDEs) based on the Liouville-Caputo derivative. We prove the existence and uniqueness of a solution for the FAFDEs. Furthermore, the stability analysis of the model is investigated and the numerical simulation is accordingly performed to support the proposed model

Optimal control of Zika virus infection by vector elimination, vector-to-human and human-to-human contact reduction

Abstract The recent outbreak of mosquito-borne Zika virus (ZIKV) in Brazil, with estimated cases surpassing 1.5 million, has gained attention due to its rapid spread and neurological complications associated with the infection such as microcephaly and Guillain-Barré syndrome. Beside vector transmission, primarily via Aedes mosquitoes, sexual transmission also contributes to the virus outbreak. The epidemiological patterns of these viruses suggest that Zika virus could cause other outbreaks, particularly in tropical regions with high vector concentration. To plan and prepare for a counter-control measure, it is important to study the previous cases. Hence, the control model is proposed from the deterministic model of Zika virus infection. Regarding control measures, the control functions for these strategies; vector elimination, vector-to-human contact reduction, and human-to-human contact reduction are introduced into the system. The necessary conditions for the optimal controls are determined using Pontryagin’s maximum principle and the optimality system is solved using Rung-Kutta fourth order scheme. Consequently, numerical results of the system with control and the system without control are shown and discussed

Model Predictive Control of COVID-19 Pandemic with Social Isolation and Vaccination Policies in Thailand

This study concerns the COVID-19 pandemic in Thailand related to social isolation and vaccination policies. The behavior of disease spread is described by an epidemic model via a system of ordinary differential equations. The invariant region and equilibrium point of the model, as well as the basic reproduction number, are also examined. Moreover, the model is fitted to real data for the second wave and the third wave of the pandemic in Thailand by a sum square error method in order to forecast the future spread of infectious diseases at each time. Furthermore, the model predictive control technique with quadratic programming is used to investigate the schedule of preventive measures over a time horizon. As a result, firstly, the plan results are proposed to solve the limitation of ICU capacity and increase the survival rate of patients. Secondly, the plan to control the outbreak without vaccination shows a strict policy that is difficult to do practically. Finally, the vaccination plan significantly prevents disease transmission, since the populations who get the vaccination have immunity against the virus. Moreover, the outbreak is controlled in 28 weeks. The results of a measurement strategy for preventing the disease are examined and compared with a control and without a control. Thus, the schedule over a time horizon can be suitably used for controlling

Sub-Optimal Control in the Zika Virus Epidemic Model Using Differential Evolution

A dynamical model of Zika virus (ZIKV) epidemic with direct transmission, sexual transmission, and vertical transmission is developed. A sub-optimal control problem to counter against the disease is proposed including three controls: vector elimination, vector-to-human contact reduction, and sexual contact reduction. Each control variable is discretized into piece-wise constant intervals. The problem is solved by Differential Evolution (DE), which is one of the evolutionary algorithm developed for optimization. Two scenarios, namely four time horizons and eight time horizons, are compared and discussed. The simulations show that models with controls lead to decreasing the number of patients as well as epidemic period length. From the optimal solution, vector elimination is the prioritized strategy for disease control

The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense

It is well known that the Black-Scholes model is used to establish the behavior of the option pricing in the financial market. In this paper, we propose the modified version of Black-Scholes model with two assets based on the Liouville-Caputo fractional derivative. The analytical solution of the proposed model is investigated by the Laplace transform homotopy perturbation method