Impact of social media advertisements on the transmission dynamics of COVID-19 pandemic in India

Abstract

In this paper, we propose a mathematical model to assess the impact of social media advertisements in combating the coronavirus pandemic in India. We assume that dissemination of awareness among susceptible individuals modifies public attitudes and behaviours towards this contagious disease which results in reducing the chance of contact with the coronavirus and hence decreasing the disease transmission. Moreover, the individual's behavioral response in the presence of global information campaigns accelerate the rate of hospitalization of symptomatic individuals and also encourage the asymptomatic individuals for conducting health protocols, such as self-isolation, social distancing, etc. We calibrate the proposed model with the cumulative confirmed COVID-19 cases for the Republic of India. We estimate eight epidemiologically important parameters, and also the size of basic reproduction number for India. We find that the basic reproduction number for India is greater than unity, which represents the substantial outbreak of COVID-19 in the country. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected population. Our results reveal that to reduce disease burden in India, non-pharmaceutical interventions strategies should be implemented effectively to decrease basic reproduction number below unity. Continuous propagation of awareness through the internet and social media platforms should be regularly circulated by the health authorities/government officials for hospitalization of symptomatic individuals and quarantine of asymptomatic individuals to control the prevalence of disease in India.

Keywords: COVID-19; Epidemic model; Estimation; Future pandemic; Global stability; Sensitivity analysis; Social media advertisements.

Fig. 1

Schematic diagram for system (1). Here, the color of the terms indicates their function. In particular, the red color denotes the impact of awareness programs on the reduction in contact rates of susceptible individuals with symptomatic/asymptomatic individuals, blue color stands for the effect of broadcasting information on awareness of susceptible individuals and green color represents the impact of awareness on the quarantine of asymptomatic individuals

Fig. 2

Plots of the output of the fitted model (1) and the observed active corona cases for India. Red dotted line shows real data points and the blue line stands for model solution. The figure shows that the cumulative number of COVID-19 increases exponentially as time progresses

Fig. 3

Global stability of the endemic equilibrium $E_{\ast }$ of system (1) in a $I_s$–$I_a$–M and b S–E–R spaces. Parameters are at the same values as in Fig. 8. Figure shows that solution trajectories starting from four different initial points ultimately converge to the components of endemic equilibrium $E_{\ast }$

Fig. 4

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 2

Fig. 5

Sensitivity quantification by calculating sensitivity coefficient through $L^2$ norm. Ranking of parameters from the most sensitive to the least ones yields the ordering ${[\sigma ,r_0,d,{\beta }_1,{\alpha }_s,\lambda ,{\varphi }_s,r,{\lambda }_0]}^T$

Fig. 6

Normalized forward sensitivity indices of ${\mathcal{R}}_0$ with respect to model parameters. Parameters are at the same values as in Table 2. A lower value of ${\mathcal{R}}_0$ is preferable since it enhances the possibility of disease eradication. Therefore, above all an increase in the parameters $\Lambda$, ${\beta }_1$, $\sigma$ and ${\lambda }_0$ must be prevented by all means, while an increase in $c_{m_s}$, a, ${\varphi }_s$, $\lambda$, ${\alpha }_s$, d and $M_0$ should instead be favored

Fig. 7

Plots of basic reproduction number (${\mathcal{R}}_0$) with respect a $\lambda$ and $M_0$, and b $c_{m_s}$ and ${\varphi }_s$. Rest of the parameters are at the same values as in Table 2. The figures show that the values of ${\mathcal{R}}_0$ can be maintained below unity by boosting up the parameters $\lambda$, $M_0$, $c_{m_s}$ and ${\varphi }_s$

Fig. 8

Contour lines representing the equilibrium values of symptomatic individuals ($I_s$) as functions of a $\Lambda$ and ${\beta }_1$, b ${\varphi }_h$ and ${\beta }_2$, c r and $r_0$, d $\lambda$ and $\delta$, e $c_{m_s}$ and p, f $c_{m_a}$ and p, g $M_0$ and ${\lambda }_0$, h ${\varphi }_s$ and ${\beta }_a$, and i ${\gamma }_a$ and $\theta$. Parameters are at the same values as in Table 2 except $\Lambda =100$, ${\beta }_1=0.000004$, ${\beta }_2=0.0000012$, $\lambda =0.0012$, $p=1200$, ${\lambda }_0=0.008$, $\sigma =0.19$, ${\gamma }_a=0.002$, $\delta =0.0005$, $d=0.00003518$, $r=0.01$, $r_0=0.005$, $M_0=500$. The figures clearly indicate that behavioral changes induced by propagation of awareness through social media advertisements can help to reduce the active symptomatic infections effectively

Fig. 9

Variation of symptomatic individuals ($I_s$) with respect to time for different values of a r and $M_0$, and b ${\varphi }_s$ and $\lambda$. Parameters are at the same values as in Fig. 8. The figures show that symptomatic infections can be completely eradicated for higher rates of hospitalization and broadcasting of information through social media advertisements