Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru

Abstract

<p style='text-indent:20px;'>Since the start of COVID-19 pandemic, the definition of normal life has changed drastically. The number of cases of this pandemic is rising everyday across the globe. In this study, we propose a compartmental model, which considers the isolation factor of Coronavirus infected individuals. The model consists of five compartments: susceptible (S), exposed (E), Infected (I), Isolated (L) and recovered (R). We have estimated the parameters of the model system and the expression of the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ R_0 $\end{document}</tex-math></inline-formula> using real data set. The exact value of the basic reproduction number is computed for India, Brazil and Peru. The local and global stability analysis of disease-free equilibrium and endemic equilibrium points is carried out. The forecasting of the pandemic is done using real data. It has been observed that to understand the pandemic the time frame has to be divided into small intervals as the parameters of the pandemic are changing with time. Within a time frame of approximately four months (i.e. from July to October 2020), the transmission rate of India has been reduced by approximately 84%. Whereas the transmission rate in Brazil and Peru has increased by 79% and 45% respectively. The sensitivity of various parameters involved in the model has been analyzed. We have presented a complete analysis to check the existence of backward bifurcation.</p>

Mathematical modeling of contact tracing and stability analysis to inform its impact on disease outbreaks; an application to COVID-19

“…Furthermore, by using the acquired values of fitted parameters in Table 3 , and expression (26) we estimated the basic reproduction number for South Korea to be 3.21, where the authors in ( Kim et al., 2020 ; Tang et al., 2022 ) suggested to be 1.77 and 2.6 respectively. For Brazil, we obtained , while it was estimated in the works ( de Souza et al., 2020 ; Kumari, Kumar, Sharma, Singh, & Parshad, 2023 ) to be 3.1. Finally, in Venezuela, we obtained , while authors in ( González-Parra, Díaz-Rodríguez, & Arenas, 2022 ) found .…”

Controlling dynamics of a COVID--19 mathematical model using a parameter switching algorithm

“…In support of this idea note that the most mathematical models of integer or even fractional order describing COVID-19 can be described by (2) as can be seen in e.g. few of the numerous works on this subject [28,29,30,31,32,33,34,35]. Moreover, the algorithm proved to be useful experimentally too [24].…”

Controlling the dynamics of a COVID‐19 mathematical model using a parameter switching algorithm

“…In this paper, it is shown how the PS algorithm can be used to obtain a stabilization of the chaotic behavior of a pandemic like COVID‐19 propagation, modeled by the relation (). In support of this idea, note that the most mathematical models of integer or even fractional order describing COVID‐19 can be presented by () as can be seen in, for example, few of the numerous works on this subject 14,33–39 . Moreover, the algorithm has been proved to be useful experimentally too 27 .…”

“…In support of this idea, note that the most mathematical models of integer or even fractional order describing COVID-19 can be presented by (2) as can be seen in, for example, few of the numerous works on this subject. 14,[33][34][35][36][37][38][39] Moreover, the algorithm has been proved to be useful experimentally too. 27 The method determines the system to change the behavior to any other of its possible regular or chaotic behavior.…”