A quantitative and qualitative analysis of the COVID-19 pandemic model (original) (raw)

Mathematical Models of COVID-19

2021

For more than a year, the COVID-19 pandemic has been a major public health issue, affecting the lives of most people around the world. With both people’s health and the economy at great risks, governments rushed to control the spread of the virus. Containment measures were heavily enforced worldwide until a vaccine was developed and distributed. Although researchers today know more about the characteristics of the virus, a lot of work still needs to be done in order to completely remove the disease from the population. However, this is true for most of the infectious diseases in existence, including Influenza, Dengue fever, Ebola, Malaria, and Zika virus. Understanding the transmission process of a disease is usually acquired through biological and chemical studies. In addition, mathematical models and computational simulations offer different approaches to predict the number of infectious cases and identify the transmission patterns of a disease. Information obtained helps provide ...

A simple mathematical model for Coronavirus (COVID-19)

medRxiv, 2020

A novel coronavirus (COVID-19) was identified in Wuhan, China in the end of 2019, it causing an outbreak of viral pneumonia. It caused to the death rate of 4:63% among 571; 678 confirmed cases around the world to the March 28th, 2020. In this brief current study, we will present a simple mathematical model where we show how the probability of successfully getting infected when coming into contact with an infected individual and the per capita contact rate affect the healthy and infected population with time. The proposed model is used to offer predictions about the behavior of COVID-19 for a shorter period of time.

Mathematical modelling for coronavirus disease (COVID-19) in predicting future behaviours and sensitivity analysis

Mathematical Modelling of Natural Phenomena

Nowadays, there are a variety of descriptive studies of available clinical data for coronavirus disease (COVID-19). Mathematical modelling and computational simulations are effective tools that help global efforts to estimate key transmission parameters. The model equations often require computational tools and dynamical analysis that play an important role in controlling the disease. This work reviews some models for coronavirus first, that can address important questions about the global health care and suggest important notes. Then, we model the disease as a system of differential equations. We develop previous models for the coronavirus, some key computational simulations and sensitivity analysis are added. Accordingly, the local sensitivities for each model state with respect to the model parameters are computed using three different techniques: non-normalizations, half normalizations and full normalizations. Results based on sensitivity analysis show that almost all model para...

Mathematical and Computer Models of the COVID-19 Epidemic

Scientific Journal of Astana IT University

The COVID-19 epidemic has gone down in history as an emergency of international importance. Currently, the number of people infected with coronavirus around the world continues to grow, and modeling such a complex system as the spread of infection is one of the most pressing problems. Various models are used to understand the progress of the COVID-19 coronavirus epidemic and to plan effective control strategies. Such models require the use of advanced computing, such as artificial intelligence, machine learning, cloud computing, and edge computing. This article uses the SIR mathematical model, which is often used and simple to model the prevalence of COVID-19 infection. The SIR model can provide a theoretical basis for studying the prevalence of the COVID-19 virus in a specific population and an understanding of the temporal evolution of the virus. One of the main advantages of this model is the ease of adjusting the sampling parameters as the study scale increases and the most appr...

A Mathematical Model of COVID-19: Analysis and Identification of Parameters for Better Decision Making

Applied Mathematics, 2022

Since the onset of the COVID-19 epidemic, the world has been impressed by two things: The number of people infected and the number of deaths. Here, we propose a mathematical model of the spread of this disease, analyze this model mathematically and determine one or more dominant factors in the propagation of the COVID-19 epidemic. We consider the S-E-I-R epidemic model in the form of ordinary differential equations, in a population structured in susceptibles S, exposed E as caregivers, travelers and assistants at public events, infected I and recovered R classes. Here we decompose the recovered class into two classes: The deaths class D and the class of those who are truly healed H. After the model construction, we have calculated the basic reproduction number 0 R , which is a function of certain number of parameters like the size of the exposed class E. In our paper, the mathematical analysis, which consists in searching the equilibrium points and studying their stability, is done. The work identifies some parameters on which one can act to control the spread of the disease. The numerical simulations are done and they illustrate our theoretical analysis.

Mathematical Model of the Transmission Dynamics of Corona Virus Disease (COVID-19) and Its Control

Asian Research Journal of Mathematics

This work is aimed at formulating a mathematical model for the transmission dynamics and control of corona virus disease in a population. The Disease Free Equilibrium state of the model was determined and shown to be locally asymptotically stable. The Endemic Equilibrium state of the model was also established and proved to be locally asymptotically stable using the trace and determinant method, after which we determined the basic reproduction number ( ) of the model using the next generation method. When ( ), the disease is wiped out of a population, but if ( ), the disease invades such population. Local sensitivity analysis result shows that the rate at which the exposed are quarantined ( ), the rate at which the infected are isolated ( ), the rate at which the quarantined are isolated ( ), and the treatment rate ( ) should be targeted by the control intervention strategies as an increase in the values of these parameters ( and ) will reduce the basic reproduction number ( ) of ...

Mathematical modeling for infectious viral disease: The COVID‐19 perspective

Journal of Public Affairs, 2020

In this study, we examined various forms of mathematical models that are relevant for the containment, risk analysis, and features of COVID-19. Greater emphasis was laid on the extension of the Susceptible-Infectious-Recovered (SIR) models for policy relevance in the time of COVID-19. These mathematical models play a significant role in the understanding of COVID-19 transmission mechanisms, structures, and features. Considering that the disease has spread sporadically around the world, causing large scale socioeconomic disruption unwitnessed in contemporary ages since World War II, researchers, stakeholders, government, and the society at large are actively engaged in finding ways to reduce the rate of infection until a cure or vaccination procedure is established. We advanced argument for the various forms of the mathematical model of epidemics and highlighted their relevance in the containment of COVID-19 at the present time. Mathematical models address the need for understanding the transmission dynamics and other significant factors of the disease that would aid policymakers to make accurate decisions and reduce the rate of transmission of the disease.

Dynamics models for identifying the key transmission parameters of the COVID-19 disease

Alexandria Engineering Journal, 2021

After the analysis and forecast of COVID-19 spreading in China, Italy, and France the WHO has declared the COVID-19 a pandemic. There are around 100 research groups across the world trying to develop a vaccine for this coronavirus. Therefore, the quantitative and qualitative analysis of the COVID-19 pandemic is needed along with the effect of rapid test infection identification on controlling the spread of COVID-19. Mathematical models with computational simulations are the 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. In this paper, we develop the models for coronavirus disease at different stages with the addition of more parameters due to interactions among the individuals. Then, some key computational simulations and sensitivity analysis are investigated. Further, the local sensitivities for each model state concerning the model parameters are computed using the model reduction techniques: the dynamical models are eventually changed with the change of parameters are represented graphically.

Mathematical modeling for novel coronavirus ( COVID ‐19) and control

Numerical Methods for Partial Differential Equations, 2020

In the present investigations, we construct a new mathematical for the transmission dynamics of corona virus (COVID-19) using the cases reported in Kingdom of Saudi Arabia for March 02 till July 31, 2020. We investigate the parameters values of the model using the least square curve fitting and the basic reproduction number is suggested for the given data is  0 ≈ 1.2937. The stability results of the model are shown when the basic reproduction number is  0 < 1. The model is locally asymptotically stable when  0 < 1. Further, we show some important parameters that are more sensitive to the basic reproduction number  0 using the PRCC method. The sensitive parameters that act as a control parameters that can reduce and control the infection in the population are shown graphically. The suggested control parameters can reduce dramatically the infection in the Kingdom of Saudi Arabia if the proper attention is paid to the suggested controls.