430 research outputs found
Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection
A human respiratory syncytial virus surveillance system was implemented in
Florida in 1999, to support clinical decision-making for prophylaxis of
premature newborns. Recently, a local periodic SEIRS mathematical model was
proposed in [Stat. Optim. Inf. Comput. 6 (2018), no.1, 139--149] to describe
real data collected by Florida's system. In contrast, here we propose a
non-local fractional (non-integer) order model. A fractional optimal control
problem is then formulated and solved, having treatment as the control.
Finally, a cost-effectiveness analysis is carried out to evaluate the cost and
the effectiveness of proposed control measures during the intervention period,
showing the superiority of obtained results with respect to previous ones.Comment: This is a preprint of a paper whose final and definite form is with
'Chaos, Solitons & Fractals', available from
[http://www.elsevier.com/locate/issn/09600779]. Submitted 23-July-2018;
Revised 14-Oct-2018; Accepted 15-Oct-2018. arXiv admin note: substantial text
overlap with arXiv:1801.0963
Ebola Model and Optimal Control with Vaccination Constraints
The Ebola virus disease is a severe viral haemorrhagic fever syndrome caused
by Ebola virus. This disease is transmitted by direct contact with the body
fluids of an infected person and objects contaminated with virus or infected
animals, with a death rate close to 90% in humans. Recently, some mathematical
models have been presented to analyse the spread of the 2014 Ebola outbreak in
West Africa. In this paper, we introduce vaccination of the susceptible
population with the aim of controlling the spread of the disease and analyse
two optimal control problems related with the transmission of Ebola disease
with vaccination. Firstly, we consider the case where the total number of
available vaccines in a fixed period of time is limited. Secondly, we analyse
the situation where there is a limited supply of vaccines at each instant of
time for a fixed interval of time. The optimal control problems have been
solved analytically. Finally, we have performed a number of numerical
simulations in order to compare the models with vaccination and the model
without vaccination, which has recently been shown to fit the real data. Three
vaccination scenarios have been considered for our numerical simulations,
namely: unlimited supply of vaccines; limited total number of vaccines; and
limited supply of vaccines at each instant of time.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Industrial and Management Optimization' (JIMO), ISSN 1547-5816
(print), ISSN 1553-166X (online). Submitted February 2016; revised November
2016; accepted for publication March 201
A Numerical Confirmation of a Fractional SEITR for Influenza Model Efficiency
The main idea of this study is to reduce the number of susceptible to infections so that ill patients can receive prompt hospitalization. Fractional SEITR was introduced for this purpose. Both endemic and disease-free equilibrium’s’ durability was examined. The fundamental reproduction number of the fractional SEITR model was determined using the next-generation matrix method. Our analytical results were supported by numerical models. Here, a graphical representation of the fractional order model is presented to validate the conclusion through numerical simulation. We have come to the conclusion that the fractional order model is more precise and provides more information about the true data of disease dynamics
Optimal control to limit the spread of COVID-19 in Italy
We apply optimal control theory to a generalized SEIR-type model. The
proposed system has three controls, representing social distancing, preventive
means, and treatment measures to combat the spread of the COVID-19 pandemic. We
analyze such optimal control problem with respect to real data transmission in
Italy. Our results show the appropriateness of the model, in particular with
respect to the number of quarantined/hospitalized (confirmed and infected) and
recovered individuals. Considering the Pontryagin controls, we show how in a
perfect world one could have drastically diminish the number of susceptible,
exposed, infected, quarantined/hospitalized, and death individuals, by
increasing the population of insusceptible/protected.publishe
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