Mathematical Analysis of a COVID-19 Epidemic Model by using Data Driven Epidemiological Parameters of Diseases Spread in India

Abstract

This paper attempts to describe the outbreak of Severe Acute Respiratory Syndrome Coronavirus 2 (COVID-19) via an epidemic model. This virus has dissimilar e¤ects in di¤erent countries.The number of new active coronavirus cases is increasing gradually across the globe. India is now in the second stage of COVID-19 spreading, it will be an epidemic very quickly if proper protection is not undertaken based on the database of the transmission of the disease. This paper is using the current data of COVID-19 for the mathematical modeling and its dynamical analysis. We bring in a new representation to appraise and manage the outbreak of infectious disease COVID-19 through SEQIR pandemic model, which is based on the supposition that the infected but undetected by testing individuals are send to quarantine during the incubation period. During the incubation period if any individual be infected by COVID-19, then that con…rmed infected individuals are isolated and the necessary treatments are arranged so that they cannot taint the other residents in the community. Dynamics of the SEQIR model is presented by basic reproduction number R 0 and the comprehensive stability analysis. Numerical results are depicted through apt graphical appearances using the data of …ve states and India.

Stochastic approach to study control strategies of Covid-19 pandemic in India

“…Taking N as constant, we can correlate the change in V as a change in D by the relation, V ∝ (1/D). The rate constant values and initial values for the SSA simulation are taken from the reference [17] (see Tables 1 and 2) after verifying the data from 21 March 2020 to 2 June 2020 [3]. The SSA simulation results of I(t) vs. time, t (in days) for India, Uttar Pradesh, Delhi, Kerala, Maharashtra and West Bengal are shown in Figures 2(a-g), 3(a-f), 4(a-f).…”

“…The classic SEIR (Susceptible, Exposed, Infected and Recovered) epidemic model [5] is therefore extended with another compartment called Quarantine (Q) to study the Covid-19 disease dynamics in India. The extended model is known as the SEQIR model [17], its schematic diagram shown in Figure 1. In this model ( Fig.…”

“…Then, the eigenvalues of the Next Generation Matrix FV −1 are 0, 0 and αΛ/(β 1 + σ 1 + d 1 )(r 1 + β 2 + d 1 ). Thus, the basic reproduction number is calculated to be R 0 = (αΛ/(β 1 + σ 1 + d 1 )(r 1 + β 2 + d 1 )) (similarly reported in [17]). Rewriting, R 0 = S 0 × α × (1/r 1 + β 2 + d 1 ) = Susceptible population at DFE × transmissibility × net duration of infectiousness, quarantining and natural death rate.…”

“…Likewise, there have been many studies on the Covid-19 pandemic in India using various mathematical models. However, most of these studies adopt deterministic methods [10][11][12][13][14][15][16][17][18][19][20][21]. On the other hand, to capture the qualitative as well as quantitative real dynamic situations to intervene in disease outbreaks, a stochastic approach needs to be employed.…”

Stay with your community: Bridges between clusters trigger expansion of COVID-19

“…We utilized the social network model, instead of the population models with differential equations, such as the SIR models, because our aim is to clarify the consequences of the actions of people that either generate, prune, or perturb the local contact within neighbors, and accordingly, to derive the knowledge required for determining appropriate measures that need to be imposed for preventing the spread of infection. This advantage of the network-based model has been highlighted by Karaivanov in [1], wherein, its differences from population-based models such as SIR [2] and its extensions [3][4][5][6][7] were clarified. Here, the effects of preventive actions such as lockdown, its release, and of infections via edges bridging far-apart nodes, on infection spread have been evaluated.…”