Search

The outbreak of a disease can lead to behavioral changes in the healthy to avert infection. We first establish a nonlinear SEIR epidemic model that incorporates the impact of individuals' behavioral response owe to information of the disease prevalence. Both the existence of equilibria and sharp sufficient conditions on stable equilibria are verified. Whereafter, the local and global sensitivity analyses are carried out to assess the relative effects of parameters on the basic reproduction number. Therewith the optimal control problem is considered to provide a theoretical basis for disease prevention and control, and the existence and uniqueness consequences for optimal control paths are demonstrated. Some numerical examples and discussions are given to support and visualize our analytical results, which can be derived that the combined use of three control measures is more effective than any single adopted control strategy to curb the spread of diseases. We also find that the information plays a crucial role in controlling infection. [ABSTRACT FROM AUTHOR]

Screening those individuals who are latent but at higher risk of rapidly developing active tuberculosis (TB) is one of the intervention measures to control the spread of TB. This work proposes a TB SVELIT (S‐Susceptible, V‐Vaccinated, E‐Early latent, L‐Late latent, I‐Infected, T‐Treated) transmission model with relapse. In particular, a complete threshold dynamical analysis for the model is performed and the existence of optimal control is obtained. Meanwhile, the validity of the model is shown by comparing the real data with the fitted curve and the future trend in the incidence of TB in China is predicted. More importantly, the effects of four strategies, including vaccination, media propaganda, screening latent individuals, and receiving treatment, are evaluated numerically. The results suggest that the above four strategies can effectively control TB and shorten the duration of the epidemic. Interestingly, treatment is more effective than vaccination in controlling TB, but media propaganda and latent screening are cheaper and easier to implement. [ABSTRACT FROM AUTHOR]

In this work, in order to identify the most effective measure and combinations of several measures to control influenza spread, we propose an SVEIAR influenza model with imperfect vaccination, media coverage and antiviral treatment. The global dynamics of the model is explored. Sensitivity analysis of the basic reproduction number and the endemic equilibrium is conducted to evaluate the effectiveness of influenza control measures. Furthermore, an optimal control problem incorporating the three measures is formulated to design optimal control strategies for influenza. The cost-effectiveness analysis reveals that combining the three measures is the most cost-effective among the strategies considered. Numerical simulations show that media propaganda can play a dominant role in curbing influenza transmission. [ABSTRACT FROM AUTHOR]

Currently, more than one million children suffer from hand, foot and mouth disease (HFMD) every year in China. And there are no effective vaccines or antiviral drugs specifically targeted HFMD. In this paper, a two stage-structured model is constructed to fit the HFMD data from 2009 to 2014 in China and obtain its optimal parameter values by the Chi-square test of statistical inference. Using the parameter values obtained can precisely and reliably forecast the clinical cases. The basic reproduction numbers for each year are more than unit, which suggests that HFMD will persist in China under the current conditions. Sensitivity analysis of the basic reproduction number is conducted to evaluate the effectiveness of HFMD control measures. Using Pontryagins maximum principle, we derive the necessary conditions for optimal control of HFMD. Further, the impact of combinations of the strategies on HFMD transmission is investigated. Finally, we find out the most cost-effective strategy though carrying out cost-effectiveness analysis. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with optimal control problems of the Bolza type for functional–differential systems governed by nonautonomous constrained neutral inclusions given in the Hale form. We develop the method of discrete approximations to derive new necessary optimality conditions for such problems in extended Euler–Lagrange and Hamiltonian forms. The results obtained are expressed in terms of robust generalized differential constructions of variational analysis introduced earlier by the first author. [Copyright &y& Elsevier]

• An SVEITR model with vaccination, fast and slow progression, incomplete treatment and relapse for TB is proposed. • Based on the data from 1988 to 2019, the basic reproduction number (R 0)of TB in the United States is 1.3763. • If R 0 > 1, the unique endemic equilibrium is globally asymptotically stable under certain conditions. • Optimal control strategies are prevention and control education, timely treatment and enhanced efficacy. • The most cost-effective strategies are timely treatment and enhanced efficacy. Tuberculosis is a chronic infectious disease with a high death rate, which has attracted worldwide attention. In this paper, we focus on the annual data of tuberculosis in the United States from 1988 to 2019. Firstly, we propose an S V E I T R dynamical model with vaccination, fast and slow progression, incomplete treatment, and relapse. Mathematical analyses show that the disease-free equilibrium is globally asymptotically stable (unstable) if R 0 ≤ 1 (if R 0 > 1). There exists a unique endemic equilibrium that is globally asymptotically stable when R 0 > 1. Next, we use the Markov-chain Monte-Carlo (MCMC) method to acquire the model's optimal parameters. From R 0 = 1.3763 , tuberculosis will not be eliminated without control measures taken in the United States. Through partial rank correlation analysis, the most sensitive parameters to the basic reproduction number are found. Based on this, we take the actual epidemic situation of tuberculosis in the United States into considerations to get the required conditions for optimal control using Pontryagin's maximum principle and cost-effectiveness analysis. Implementation of three public health measures: tuberculosis prevention and control education, timely treatment, and enhanced efficacy can reduce the prevalence of tuberculosis in the United States. But at present, it is challenging for us to achieve the goal of eliminating tuberculosis by 2030 as called for by WHO. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with equality and inequality endpoint constraints and multivalued initial conditions. We use the method of discrete approximations and advanced tools of variational analysis and generalized differentiation in infinite dimensions to derive necessary optimality conditions in the extended Euler–Lagrange form. This method is fully realized for the delay-differential systems under consideration. [Copyright &y& Elsevier]