6 results
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2. Control of COVID-19 outbreak using an extended SEIR model.
- Author
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McQuade, Sean T., Weightman, Ryan, Merrill, Nathaniel J., Yadav, Aayush, Trélat, Emmanuel, Allred, Sarah R., and Piccoli, Benedetto
- Subjects
COVID-19 pandemic ,CONTACT tracing ,SOCIAL distancing ,DEATH rate ,ECONOMIC activity - Abstract
The outbreak of COVID-19 resulted in high death tolls all over the world. The aim of this paper is to show how a simple SEIR model was used to make quick predictions for New Jersey in early March 2020 and call for action based on data from China and Italy. A more refined model, which accounts for social distancing, testing, contact tracing and quarantining, is then proposed to identify containment measures to minimize the economic cost of the pandemic. The latter is obtained taking into account all the involved costs including reduced economic activities due to lockdown and quarantining as well as the cost for hospitalization and deaths. The proposed model allows one to find optimal strategies as combinations of implementing various non-pharmaceutical interventions and study different scenarios and likely initial conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
3. The Use of Interactive Graphics To Solve Numerical Problems.
- Author
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Lawson, C. L. and Smith, L. B.
- Subjects
INTERACTIVE computer systems ,COMPUTATIONAL mathematics ,ELECTRONIC systems ,COMPUTER systems ,ELECTRONIC data processing ,ARTIFICIAL languages ,COMPUTER graphics ,LEAST squares - Abstract
With the advent of on-line (time-sharing) computer systems and graphic terminals, we have available a new dimension in numerical problem solving capabilities. Rather than simply use the new power to achieve fast turnaround, we can develop interactive routines which are easy to use and also take advantage of the insight and visual capabilities of the human problem solver. Several on-line systems for general purpose mathematical problem solving have already been implemented as well as some special purpose systems for solving problems in a particular area such as ordinary differential equations. The advantage of restricting the problem area is that the interface with a user can be greatly simplified, in this paper we discuss some of the advantages accrued by such systems and design considerations for interactive routines. Furthermore, an implementation of an on-line least squares data-fitting program, PEG, is presented with results obtained from empirical data. In conclusion, areas for future work in this field are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 1970
4. Modeling the cytotoxicity of Romidepsin reveals the ineffectiveness of this drug in the "shock and kill" strategy.
- Author
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Deng, Qi, Guo, Ting, Qiu, Zhipeng, and Chen, Yuming
- Subjects
- *
HIV , *T cells , *HIV infections , *VIRAL load , *MULTISCALE modeling - Abstract
The "shock and kill" strategy is being widely explored to purge Human Immunodeficiency Virus (HIV) latent reservoirs. Romidepsin, a kind of latency-reversing agents (LRAs), has been shown to induce HIV RNA transcription. However, several clinical trials testing this drug have resulted in limited effect in reducing the HIV latent reservoirs. To understand the mechanisms underlying such limited effect, we develop a multi-scale model that incorporates pharmacokinetics and considers the toxicity of romidepsin to T cells in this paper. By fitting the model to the viral load data from plasma of six patients received romidepsin, we find that the model with T cell toxicity of romidepsin can well explain the clinical data. The dynamics of latently infected cells during romidepsin administration are explored using the best-fit parameter values. The results show that latently infected cells decrease very slowly and remain very stable overall in four of the six participants under the assumption of T cell toxicity of romidepsin. This implies that the ineffectiveness of romidepsin on latent reservoirs can be explained by its toxicity to T cells. In the remaining two participants, however, latently infected cells are quite stable without T cell toxicity of LRAs. It is found that the estimated activation rate of latently infected cells by romidepsin and the estimated elimination rate of romidepsin on immune cells for these two patients are very different from those for the other four patients. Thus we speculate that the heterogeneous response to romidepsin across participants may also be a determining factor of the effectiveness of romidepsin. These results may have significant implications in the search for the control of HIV infection. • An HIV model is proposed to understand the cause of ineffectiveness of romidepsin in the "shock and kill" strategy. • The model has a good fit to patients' data when T cell toxicity of romidepsin is considered. • The toxicity of romidepsin to T cell may contribute to the ineffectiveness of "shock and kill" strategy concerning romidepsin. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
5. Analysis of COVID‐19 and comorbidity co‐infection model with optimal control.
- Author
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Omame, Andrew, Sene, Ndolane, Nometa, Ikenna, Nwakanma, Cosmas I., Nwafor, Emmanuel U., Iheonu, Nneka O., and Okuonghae, Daniel
- Subjects
COVID-19 ,MIXED infections ,COMORBIDITY ,CONTINUOUS time models ,REINFECTION - Abstract
In this work, we develop and analyze a mathematical model for the dynamics of COVID‐19 with re‐infection in order to assess the impact of prior comorbidity (specifically, diabetes mellitus) on COVID‐19 complications. The model is simulated using data relevant to the dynamics of the diseases in Lagos, Nigeria, making predictions for the attainment of peak periods in the presence or absence of comorbidity. The model is shown to undergo the phenomenon of backward bifurcation caused by the parameter accounting for increased susceptibility to COVID‐19 infection by comorbid susceptibles as well as the rate of reinfection by those who have recovered from a previous COVID‐19 infection. Simulations of the cumulative number of active cases (including those with comorbidity), at different reinfection rates, show infection peaks reducing with decreasing reinfection of those who have recovered from a previous COVID‐19 infection. In addition, optimal control and cost‐effectiveness analysis of the model reveal that the strategy that prevents COVID‐19 infection by comorbid susceptibles is the most cost‐effective of all the control strategies for the prevention of COVID‐19. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
6. A two-dimensional multi-class traffic flow model
- Author
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Simone Göttlich and Caterina Balzotti
- Subjects
Statistics and Probability ,Scheme (programming language) ,Discretization ,Computer science ,two-dimensional model ,Type (model theory) ,Space (mathematics) ,Riemann problems ,data-fitting ,symbols.namesake ,Macroscopic traffic flow ,Overtaking ,FOS: Mathematics ,Applied mathematics ,Mathematics - Numerical Analysis ,90B20, 35L65, 35Q91 ,computer.programming_language ,Conservation law ,Applied Mathematics ,General Engineering ,Numerical Analysis (math.NA) ,Computer Science Applications ,Riemann hypothesis ,multi-class model ,symbols ,Curve fitting ,computer ,Macroscopic traffic flow, two-dimensional model, multi-class model, Riemann problems, data-fitting - Abstract
The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations of vehicles. Starting from the paper [20], where a two-dimensional model for a single class of vehicles is proposed, we extend the dynamics to a multi-class model leading to a coupled system of conservation laws in two space dimensions. Besides the study of the Riemann problems we also present a Lax-Friedrichs type discretization scheme recovering the theoretical results by means of numerical tests. We calibrate the multi-class model with real data and compare the fitted model to the real trajectories. Finally, we test the ability of the model to simulate the overtaking of vehicles., 21 pages, 14 figures
- Published
- 2021
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