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

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.

MODELING OF EPIDEMICS-COVID-19 USING DIFFERENTIAL EQUATIONS (Atena Editora)

MODELING OF EPIDEMICS-COVID-19 USING DIFFERENTIAL EQUATIONS (Atena Editora), 2023

The study of epidemics since ancient times is an area that has aroused great interest; the history of humanity has been marked by major infections such as smallpox, the Black Death, measles, AIDS, cholera, Ebola and others. Humanity is being hit by epidemic outbreaks, which worries the World Health Organization due to the increase in the number of cases, with the Sars-CoV-2 coronavirus becoming a global pandemic on January 30, 2020. The same one that has captured the attention of The scientific community worldwide severe acute respiratory syndrome caused by the 2019-nCoV virus or Sars-CoV - 2, results in substantial morbidity and mortality. Coronaviruses can cause diseases in humans and animals, they are a large family of viruses, their impact on humans results in respiratory infections, the recently discovered coronavirus causes the COVID-19 disease. To understand the dynamics of the epidemic allows us to design new measures that can be applied in order to combat the epidemiological outbreak, through mathematical modeling using differential equations as a tool used. to monitor the dynamics of the epidemiological behavior of Covid-19 in Ecuador. This research is developed through the explicit solution of the SIR model, and we model the development of short-term and more extensive epidemics such as COVID-19 in early stages and its best-known variants to predict the spread of infectious diseases in a population, both from the theoretical and computational point of view. Information about the Coronavirus was obtained from the Johns Hopkins University database.(Universidad Johns Hopkins, 2020)

A study on the spread of COVID 19 outbreak by using mathematical modeling

Results in Physics, 2020

Mathematical models are mainly used to depict real world problems that humans encounter in their daily explorations, investigations and activities. However, these mathematical models have some limitations as indeed the big challenges are the conversion of observations into mathematical formulations. If this conversion is inefficient, then mathematical models will provide some predictions with deficiencies. A specific real-world problem could then have more than one mathematical model, each model with its advantages and disadvantages. In the last months, the spread of covid-19 among humans have become fatal, destructive and have paralyzed activities across the globe. The lockdown regulations and many other measures have been put in place with the hope to stop the spread of this deathly disease that have taken several souls around the globe. Nevertheless, to predict the future behavior of the spread, humans rely on mathematical models and their simulations. While many models, have been suggested, it is important to point out that all of them have limitations therefore newer models can still be suggested. In this paper, we examine an alternative model depicting the spread behavior of covid-19 among humans. Different differential and integral operators are used to get different scenarios.

A Model for the Spread of Infectious Diseases with Application to COVID-19

Challenges

Given the present pandemic caused by the severe acute respiratory syndrome coronavirus 2 or SARS-CoV-2 virus, the authors tried fitting existing models for the daily loss of lives. Based on data reported by Worldometers on the initial stages (first wave) of the pandemic for countries acquiring the disease, the authors observed that the logarithmic rendering of their data hinted the response of a first-order process to a step function input, which may be modeled by a three-parameters function, as described in this paper. This model was compared against other similar, log(N)-class of models that are non-compartmental type (such as the susceptible, infected, and removed, or SIR models), obtaining good fit and statistical comparison results, where N denotes the cumulative number of daily presumed deaths. This simple first-order response model can also be applied to bacterial and other biological growth phenomena. Here we describe the model, the numerical methods utilized for its applica...

Mathematical Modelling in Prediction of Novel CoronaVirus (COVID-19) Transmission Dynamics

2020

Human civilizations are under enormous threats due to the outbreak of novel coronavirus (COVID-19) originated from Wuhan, China. The asymptomatic carriers are the potential spreads of this novel virus. Since, guaranteed antiviral treatments have not been available in the market so far, it is really challenging to fight against this contagious disease. To save the living mankind, it is urgent to know more about how the virus transmits itself from one to another quite rapidly and how we can predict future infections. Scientists and Researchers are working hard in investigating to understand its high infection rate and transmission process. One possible way to know is to use our existing COVID-19 infection data and prepare a useful model to predict the future trend. Mathematical modelling is very useful to understand the basic principle of COVID-19 transmission and provide necessary guidelines for future prediction. Here, we have reviewed 9 distinct commonly used models based on Mathem...

Mathematical Model of Novel COVID-19 and Its Transmission Dynamics

In this paper, we formulated a dynamical model of COVID-19 to describe the transmission dynamics of the disease. The well possedness of the formulated model equations was proved. Both local and global stability of the disease free equilibrium and endemic equilibrium point of the model equation was established using basic reproduction number. The results show that, if the basic reproduction number is less than one then the solution converges to the disease free steady state i.e. the disease free equilibrium is asymptotically stable. The endemic states are considered to exist when the basic reproduction number for each disease is greater than one. Numerical simulation carried out on the model revealed that an increase in level of contact rate among individuals has an effect on reducing the prevalence of COVID-19 and COVID-19 disease. Furthermore, sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on the transmission dynamics of COVID-19.