Background: COVID-19 is an emerging disease and precise data are not available in the world and Iran. this study aimed to determine the epidemic trend and prediction of COVID-19 in Iran. Methods: This study is a secondary data analysis and modeling. We used the daily reports of definitive COVID-19 patients (sampling of severe cases and hospitalization) released by Iran Ministry of Health and Medical Education. Epidemic projection models of Gompertz, Von Bertalanffy and least squared error (LSE) were used to predict the number of cases at April 3, 2020 until May 13, 2020. Results: R0 in Iran was estimated to be 4.7 that has now fallen to below 2. Given the three different scenarios, the prediction of the patients on April 3, 2020 by Von Bertalanffy, Gompertz and LSE were estimated at 48200, 52500 and 58000, respectively. The number of deceased COVID-19 patients was also estimated to be 3600 individuals using the Von growth model, 4200 ones by Gompertz's model and 4850 ones according to the LSE method. To predict and estimate the number of patients and deaths in the end of epidemic based on Von and Gompertz models, we will have 87000 cases, 4900 and 11000 deaths until 13 May and 1 June, respectively. Conclusion: The process of controlling the epidemic is tangible. If enforcement and public behavior interventions continue with current trends, the control and reduction of the COVID-19 epidemic in Iran will be flat from April 28, until July, 2020 and new cases are expected to decline from the following Iranian new year.
A greedy algorithm in combination with radial basis functions partition of unity collocation (GRBF‐PUC) scheme is used as a locally meshless method for American option pricing. The radial basis function partition of unity method (RBF‐PUM) is a localization technique. Because of having interpolation matrices with large condition numbers, global approximants and some local ones suffer from instability. To overcome this, a greedy algorithm is added to RBF‐PUM. The greedy algorithm furnishes a subset of best nodes among the points X. Such nodes are then used as points of trial in a locally supported RBF approximant for each partition. Using of greedy selected points leads to decreasing the condition number of interpolation matrices and reducing the burdensome in pricing American options.
In this article, we use some greedy algorithms to avoid the ill‐conditioning of the final linear system in unsymmetric Kansa collocation method. The greedy schemes have the same background, but we use them in different settings. In the first algorithm, the optimal trial points for interpolation obtained among a huge set of initial points are used for numerical solution of partial differential equations (PDEs). In the second algorithm, based on the Kansa's method, the PDE is discretized to a finite number of test functional equations, and a greedy sparse discretization is applied for approximating the linear functionals. Each functional is stably approximated by some few trial points with an acceptable accuracy. The third greedy algorithm is used to generate the test points. This paper shows that the greedily selection of nodes yields a better conditioning in contrast with usual full meshless methods. Some well‐known PDE examples are solved and compared with the full unsymmetric Kansa's technique. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1884–1899, 2017
In this paper, we develop a fractional-order differential model for the dynamics of immune responses to SARS-CoV-2 viral load in one host. In the model, a fractional-order derivative is incorporated to represent the effects of temporal long-run memory on immune cells and tissues for any age group of patients. The population of cytotoxic T-cells (CD8+), natural killer (NK) cells and infected viruses are unknown in this model. Some interesting sufficient conditions that ensure the asymptotic stability of the steady states are obtained. This model indicates some complex phenomena in COVID-19 such as "immune exhaustion" and "Long COVID". Sensitivity analysis is also investigated for model parameters to determine the parameters that are effective in determining of the long COVID duration, disease control and future treatment as well as vaccine design. The model is verified with clinical and experimental data of 5 patients with COVID-19.
In this study, a mathematical, fractional-order model was developed for B cell chronic lymphocytic leukemia, with immune system, and then analyzed. Interactions between B leukemia cells, natural killer cells, cytotoxic T cells, and T-helper cells are considered to be incorporated into a system consisting of four fractional differential equations. For estimation of the parameters, clinical data of six patients were used. By numerical solution of the system, the interactions between the leukemia cell population and the immune system cell populations for values of ∈ (0, 1) at different times were explained. By determining points of equilibrium and stability of the system were met. Bifurcation analysis showed that use of the fractional-order model, figure out unpredictable behaviors of the system such as saddle-node, bistability and hysteresis phenomenon occurred in the system by changing the values of some of the parameters, it was predictable. KEYWORDS bifurcation, chronic lymphocytic leukemia, mathematical model of fractional-order, stability analysis MSC CLASSIFICATION 92XX; 92Bxx 1 INTRODUCTION 1.1 Chronic lymphocytic leukemia background B cell chronic lymphocytic leukemia (B-CLL) is a progressive and malignant disease of the hematopoietic organs of the body. The disease is caused by the impaired proliferation and development of white blood cell and its precursors in the blood, bone marrow, spleen, and lymph nodes. The excess production of blood cell is abnormal in bone marrow leukemia. These cells differ from blood cells and do not function appropriately. Consequently, the production of normal white blood cells stops and eliminates the individual's ability to cope with disease. Leukemia cancer cells also have a negative effect on the production of other types of blood cells that are produced by the bone marrow, including red blood cells, which transport oxygen to the tissues of the body, and blood platelets, which prevent blood clotting. Therefore, in a variety of leukemia, weak immunity, anemia, and impaired blood clotting may occur. 1,2 Given the fact that there is no proper theory of cancer, scientific advances in the treatment of this disease are almost confined to trial and error, and clinical tests are used to diagnose drug efficacy.
In this paper, we develop a fractional-order differential model for the dynamics of immune responses to SARS-CoV-2 viral load in one host. In the model, a fractional-order derivative is incorporated to represent the effects of temporal long-run memory on immune cells and tissues for any age group of patients. The population of cytotoxic T cells (CD 8 + ), natural killer (NK) cells, and infected viruses is unknown in this model. Some interesting sufficient conditions that ensure the asymptotic stability of the steady states are obtained. This model indicates some complex phenomena in COVID-19 such as “immune exhaustion” and “long COVID.” Sensitivity analysis is also investigated for model parameters to determine the parameters that are effective in disease control and future treatment as well as vaccine design. The model is verified with clinical and experimental data of 5 patients with COVID-19.
Background: COVID-19 has been deeply affecting people's lives all over the world.It is significant for prevention and control to model the evolution effectively and efficiently. Methods:We first propose the multi-chain Fudan-CCDC model which is based on the original Fudan-CCDC model to describe the revival of COVID-19 in some countries.Multi-chains are considered as the superposition of distinctive single chains. Parameter identification is carried out by minimizing the penalty function.Results: From results of numerical simulations, the multi-chain model performs well on data fitting and reasonably interprets the revival phenomena. The band of ±25% 1 All rights reserved. No reuse allowed without permission. : medRxiv preprint fluctuation of simulation results could contain most seemly unsteady increments. Conclusion:The multi-chain model has better performance on data fitting in revival situations compared with the single-chain model. It is predicted by the three-chain model with data by Apr 21 that the epidemic curve of Iran would level off on round May 10, and the final cumulative confirmed cases would be around 88820. The upper bound of the 95% confidence interval would be around 96000.Keywords: COVID-19; Iran; multi-chain Fudan-CCDC model. conceived the study, carried out the analysis, discussed the results, drafted the first manuscript, critically read and revised the manuscript, and gave final approval for publication.
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