Dynamics of coronavirus pandemic: effects of community awareness and global information campaigns

Abstract

The effects of social media advertisements together with local awareness in controlling COVID-19 are explored in the present investigation by means of a mathematical model. The expression for the basic reproduction number is derived. Sufficient conditions for the global stability of endemic equilibrium are obtained. We perform sensitivity analysis to identify the key parameters of the model having great impacts on the prevalence and control of COVID-19. We calibrate the proposed model to fit the data set of COVID-19 cases for India. Our simulation results show that dissemination rate of awareness among susceptible individuals at community level and individual level plays pivotal role in curtailing the COVID-19 disease. Moreover, we observe that the global information distributing from social media and local awareness coming from mouth-to-mouth communication between unaware susceptible and aware people, together with hospitalization of symptomatic individuals and quarantine of asymptomatic individuals, are much beneficial in reducing COVID-19 cases in India. Our study suggests that both global and local awareness must be implemented effectively to manage the burden of COVID-19 pandemic.

Fig. 1

Schematic diagram of the system (1). Here, the mathematical terms in red color represent the impact of social media advertisements in modifying human behavior; the outward arrows indicate the death of individuals in different classes of human population that includes natural death of human population and their COVID-19-induced death

Fig. 2

Semi-relative sensitivities of the symptomatic infected population with respect to model parameters using automatic differentiation. The observation window is [0, 400], and the sensitivity of a parameter is identified by the maximum deviation of the state variable (along y-axis), and it also identifies the time intervals when the system is most sensitive to such changes. Parameters are at the same values as in Table 4

Fig. 3

Sensitivity quantification by calculating sensitivity coefficient through $L^2$ norm

Fig. 4

Plots of the output of the fitted model (1) and the observed active coronavirus cases for India during period February 01, 2021, to May 22, 2021. Here, the magenta dotted line shows real data points, and the blue line stands for solution of model (1). The figure shows that the cumulative number of active COVID-19 cases increases exponentially as time progresses

Fig. 5

Variation of symptomatic individuals ($I_s$) with respect to time for different values of a ${\gamma }_a$, b ${\varphi }_s$ and (c) $\rho$. Rest of the parameters are at the same values as in Table 4 except in a $p=12$, $q=4$, ${\lambda }_{01}=0.004$, b, c $p=1200$, ${\lambda }_{01}=0.004$

Fig. 6

Contour lines representing the equilibrium values of symptomatic individuals ($I_s$) as functions of a ${\beta }_2$ and ${\gamma }_a$, b $\rho$ and ${\lambda }_{01}$, c $M_0$ and ${\lambda }_{02}$, d r and $r_0$, e $\lambda$ and p, f $\Lambda$ and ${\beta }_1$, g ${\varphi }_s$ and ${\sigma }_1$, h ${\varphi }_h$ and ${\beta }_a$, and i ${\sigma }_2$ and ${\sigma }_3$. Rest of the parameters are at the same values as in Table 4 except in a, c, e $p=12$, $q=4$, $a=0.1$, ${\lambda }_{01}=0.004$, (b) $p=12$, $q=4$, d, f, g, h, i $p=12$, $q=4$, ${\lambda }_{01}=0.004$

Fig. 7

Global stability of the endemic equilibrium $E_{\ast }$ of system (2) in a $I_s$–$I_a$–M and b S–Q–H spaces. Parameters are at the same values as in Table 4 except in a $p=12$, $q=4$, $a=0.1$, ${\lambda }_{01}=0.004$, and b $p=12$, $q=4$, ${\lambda }_{01}=0.004$