ABSTRACT
BACKGROUND: We provide a compartmental model for the transmission of some contagious illnesses in a population. The model is based on partial differential equations, and takes into account seven sub-populations which are, concretely, susceptible, exposed, infected (asymptomatic or symptomatic), quarantined, recovered and vaccinated individuals along with migration. The goal is to propose and analyze an efficient computer method which resembles the dynamical properties of the epidemiological model. MATERIALS AND METHODS: A non-local approach is utilized for finding approximate solutions for the mathematical model. To that end, a non-standard finite-difference technique is introduced. The finite-difference scheme is a linearly implicit model which may be rewritten using a suitable matrix. Under suitable circumstances, the matrices representing the methodology are M-matrices. RESULTS: Analytically, the local asymptotic stability of the constant solutions is investigated and the next generation matrix technique is employed to calculate the reproduction number. Computationally, the dynamical consistency of the method and the numerical efficiency are investigated rigorously. The method is thoroughly examined for its convergence, stability, and consistency. CONCLUSIONS: The theoretical analysis of the method shows that it is able to maintain the positivity of its solutions and identify equilibria. The method's local asymptotic stability properties are similar to those of the continuous system. The analysis concludes that the numerical model is convergent, stable and consistent, with linear order of convergence in the temporal domain and quadratic order of convergence in the spatial variables. A computer implementation is used to confirm the mathematical properties, and it confirms the ability in our scheme to preserve positivity, and identify equilibrium solutions and their local asymptotic stability.
Subject(s)
Models, Theoretical , Quarantine , Humans , Computer Simulation , VaccinationABSTRACT
The spreading of COVID-19 became a global issue that had a significant impact on health, life, and economic sectors. Efforts from all over the world are focused on discussing a variety of healthcare approaches to reduce the effect of COVID-19 among individuals. Mathematical tools with numerical simulations are important approaches that help international efforts to determine critical transmission factors as well as controlling the virus spread. In this paper, we develop a mathematical model that considers a vaccination compartment in terms of ordinary differential equations. This study focuses on the real data of confirmed cases in Kurdistan Region of Iraq from July 17th, 2021 to January 1st, 2022. Model results and real data for the total number of infected people were compared using computational tools in MATLAB. Additionally, non-normalization, half-normalization, and full-normalization methods are used to determine the local sensitivities between model variables and parameters. Interestingly, computational results show that the dynamics of model results and real confirmed cases are very close to each other. Accordingly, the elasticity coefficients provide a great understanding of the impact of vaccination on transmissions. The model results here can also help international efforts for further suggestions and improvements to control this disease more effectively. © Palestine Polytechnic University-PPU 2023.
ABSTRACT
The spread of the COVID-19 pandemic has been considered as a global issue. Based on the reported cases and clinical data, there are still required international efforts and more preventative measures to control the pandemic more effectively. Physical contact between individuals plays an essential role in spreading the coronavirus more widely. Mathematical models with computational simulations are effective tools to study and discuss this virus and minimize its impact on society. These tools help to determine more relevant factors that influence the spread of the virus. In this work, we developed two computational tools by using the R package and Python to simulate the COVID-19 transmissions. Additionally, some computational simulations were investigated that provide critical questions about global control strategies and further interventions. Accordingly, there are some computational model results and control strategies. First, we identify the model critical factors that helps us to understand the key transmission elements. Model transmissions can significantly be changed for primary tracing with delay to isolation. Second, some types of interventions, including case isolation, no intervention, quarantine contacts and quarantine contacts together with contacts of contacts are analyzed and discussed. The results show that quarantining contacts is the best way of intervening to minimize the spread of the virus. Finally, the basic reproduction number R0 is another important factor which provides a great role in understanding the transmission of the pandemic. Interestingly, the current computational simulations help us to pay more attention to critical model transmissions and minimize their impact on spreading this disease. They also help for further interventions and control strategies.
ABSTRACT
Spreading COVID-19 pandemic has been considered as a global issue. Many international efforts including mathematical approaches have been recently discussed to control this disease more effectively. In this study, we have developed our previous SIUWR model and some transmission parameters are added. Accordingly, the basic reproduction number and elasticity coefficients are calculated at the equilibrium points. Then, some key critical model parameters are identified based on local sensitivities. In addition, the validation of the suggested model is checked by comparing some collected real data in Iraq and France from January 1st, 2021 to December 25th, 2021. Interestingly, there are good agreements between the model results and the real confirmed data using computational simulations in MATLAB. Results provide some biological interpretations and they can be used to control this pandemic more effectively. The model results will be used for both countries in minimizing the impact of this virus on their communities.
ABSTRACT
Numerical simulations have revolutionized research in several engineering areas by contributing to the understanding and improvement of several processes, being biomedical engineering one of them. Due to their potential, computational tools have gained visibility and have been increasingly used by several research groups as a supporting tool for the development of preclinical platforms as they allow studying, in a more detailed and faster way, phenomena that are difficult to study experimentally due to the complexity of biological processes present in these models-namely, heat transfer, shear stresses, diffusion processes, velocity fields, etc. There are several contributions already in the literature, and significant advances have been made in this field of research. This review provides the most recent progress in numerical studies on advanced microfluidic devices, such as organ-on-a-chip (OoC) devices, and how these studies can be helpful in enhancing our insight into the physical processes involved and in developing more effective OoC platforms. In general, it has been noticed that in some cases, the numerical studies performed have limitations that need to be improved, and in the majority of the studies, it is extremely difficult to replicate the data due to the lack of detail around the simulations carried out.
ABSTRACT
Global efforts around the world are focused on to discuss several health care strategies for minimizing the impact of the new coronavirus (COVID-19) on the community. As it is clear that this virus becomes a public health threat and spreading easily among individuals. Mathematical models with computational simulations are effective tools that help global efforts to estimate key transmission parameters and further improvements for controlling this disease. This is an infectious disease and can be modeled as a system of non-linear differential equations with reaction rates. This work reviews and develops some suggested models for the COVID-19 that can address important questions about global health care and suggest important notes. Then, we suggest an updated model that includes a system of differential equations with transmission parameters. Some key computational simulations and sensitivity analysis are investigated. Also, the local sensitivities for each model state concerning the model parameters are computed using three different techniques: non-normalizations, half normalizations, and full normalizations. Results based on the computational simulations show that the model dynamics are significantly changed for different key model parameters. Interestingly, we identify that transition rates between asymptomatic infected with both reported and unreported symptomatic infected individuals are very sensitive parameters concerning model variables in spreading this disease. This helps international efforts to reduce the number of infected individuals from the disease and to prevent the propagation of new coronavirus more widely on the community. Another novelty of this paper is the identification of the critical model parameters, which makes it easy to be used by biologists with less knowledge of mathematical modeling and also facilitates the improvement of the model for future development theoretically and practically.