ABSTRACT
It is of great curiosity to observe the effects of prevention methods and the magnitudes of the outbreak including epidemic prediction, at the onset of an epidemic. To deal with COVID-19 Pandemic, an SEIQR model has been designed. Analytical study of the model consists of the calculation of the basic reproduction number and the constant level of disease absent and disease present equilibrium. The model also explores number of cases and the predicted outcomes are in line with the cases registered. By parameters calibration, new cases in Pakistan are also predicted. The number of patients at the current level and the permanent level of COVID-19 cases are also calculated analytically and through simulations. The future situation has also been discussed, which could happen if precautionary restrictions are adopted.
ABSTRACT
In this paper we consider ant-eating pangolin as a possible source of the novel corona virus (COVID-19) and propose a new mathematical model describing the dynamics of COVID-19 pandemic. Our new model is based on the hypotheses that the pangolin and human populations are divided into measurable partitions and also incorporates pangolin bootleg market or reservoir. First we study the important mathematical properties like existence, boundedness and positivity of solution of the proposed model. After finding the threshold quantity for the underlying model, the possible stationary states are explored. We exploit linearization as well as Lyapanuv function theory to exhibit local stability analysis of the model in terms of the threshold quantity. We then discuss the global stability analyses of the newly introduced model and found conditions for its stability in terms of the basic reproduction number. It is also shown that for certain values of R 0 , our model exhibits a backward bifurcation. Numerical simulations are performed to verify and support our analytical findings.
ABSTRACT
The worldwide association of health (WHO) has stated that COVID-19 (the novel coronavirus disease-2019) as a pandemic. Here, the common SEIR model is generalized in order to show the dynamics of COVID-19 transmission taking into account the ABO blood group of the infected people. Fractional order Caputo derivative are used in the proposed model. Our study is guided by the results that have been obtained by Chen J, Fan H, Zhang L, et al. from three unique medical clinics in Wuhan and Shenzhen, China. In this study, the feasibility region of the proposed model are calculated plus the points of equilibrium. Also, the equilibrium points stability is examined. A unique solution existence for the proposed paradigm is proved via utilizing the fixed point theory with regards to Caputo fractional derivative. Numerical experiments of the proposed paradigm is done and we show its sensitivity to the fractional order.
ABSTRACT
We develop a new mathematical model by including the resistive class together with quarantine class and use it to investigate the transmission dynamics of the novel corona virus disease (COVID-19). Our developed model consists of four compartments, namely the susceptible class, S ( t ) , the healthy (resistive) class, H ( t ) , the infected class, I ( t ) and the quarantine class, Q ( t ) . We derive basic properties like, boundedness and positivity, of our proposed model in a biologically feasible region. To discuss the local as well as the global behaviour of the possible equilibria of the model, we compute the threshold quantity. The linearization and Lyapunov function theory are used to derive conditions for the stability analysis of the possible equilibrium states. We present numerical simulations to support our investigations. The simulations are compared with the available real data for Wuhan city in China, where the infection was initially originated.
ABSTRACT
In the work, author's presents a very significant and important issues related to the health of mankind's. Which is extremely important to realize the complex dynamic of inflected disease. With the help of Caputo fractional derivative, We capture the epidemiological system for the transmission of Novel Coronavirus-19 Infectious Disease (nCOVID-19). We constructed the model in four compartments susceptible, exposed, infected and recovered. We obtained the conditions for existence and Ulam's type stability for proposed system by using the tools of non-linear analysis. The author's thoroughly discussed the local and global asymptotical stabilities of underling model upon the disease free, endemic equilibrium and reproductive number. We used the techniques of Laplace Adomian decomposition method for the approximate solution of consider system. Furthermore, author's interpret the dynamics of proposed system graphically via Mathematica, from which we observed that disease can be either controlled to a large extent or eliminate, if transmission rate is reduced and increase the rate of treatment.