key: cord-0962799-cvxy0xob
authors: Agusto, F.; Numfor, E.; Karthik, S.; Iboi, E.; Fulk, A.; Saint Onge, J. M.; Peterson, T.
title: Impact of public sentiments on the transmission of COVID-19 across a geographical gradient
date: 2021-02-01
journal: nan
DOI: 10.1101/2021.01.29.21250655
sha: 3991e88306bf9fc2f98eacad11407a4de5b554f5
doc_id: 962799
cord_uid: cvxy0xob

COVID-19 is a respiratory disease caused by a recently discovered, novel coronavirus, SARS-COV2. The disease has led to over 81 million confirmed cases of COVID-19, with close to 2 million deaths. In the current social climate, the risk of COVID-19 infection is driven by individual and public perception of risk and sentiments. A number of factors influences public perception, including an individual's belief system, prior knowledge about a disease and information about a disease. In this paper, we develop a model for COVID-19 using a system of ordinary differential equations following the natural history of the infection. The model uniquely incorporates social behavioral aspects such as quarantine and quarantine violation. The model is further driven by people's sentiments (positive and negative) which accounts for the influence of disinformation. People's sentiments were obtained by parsing through and analyzing COVID-19 related tweets from Twitter, a social media platform across six countries. Our results show that our model incorporating public sentiments is able to capture the trend in the trajectory of the epidemic curve of the reported cases. Furthermore, our results show that positive public sentiments reduce disease burden in the community. Our results also show that quarantine violation and early discharge of the infected population amplifies the disease burden on the community. Hence, it is important to account for public sentiment and individual social behavior in epidemic models developed to study diseases like COVID-19.

the rate ν H . The removed class (R(t)) tracks either the recovered at the rates γ I , γ A , γ Q , γ H 122 or those that have died due to COVID-19 at the rates δ I , δ A , δ Q , δ H from the symptomatic, 123 asymptomatic, quarantined, and hospitalized classes. The equations of the mathematical 124 model are given in equation (1).

where N (t) = S(t) + E(t) + I(t) + A(t) + Q(t) + H(t) + R(t). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. ; https://doi.org/10.1101/2021.01.29.21250655 doi: medRxiv preprint Variable Description

Number of susceptible individuals E(t) Number of exposed individuals A(t)

Number of asymptomatic infectious individuals I(t)

Number of symptomatic infectious individuals Q(t)

Number of quarantined individuals H(t)

Number of hospitalized individuals R(t)

Number of recovered individuals Parameter Description β Infection rate η A Infection modification parameter for the asymptomatic infection rate η Q Infection modification parameter for the quarantined infection rate q Proportion of exposed developing asymtomatic infections σ Disease progression rate from the exposed to either asymptomatic or infectious γ I 

where, k 1 = γ I + ω Q + ω H + δ I , k 2 = γ A + δ A , k 3 = ν Q + γ Q + δ Q , k 4 = ν H + γ H + δ H .

control and contain the disease. Italy instituted a lockdown on March 9, Brazil March 17, model was fitted to the two different time periods, the first period is the time before each of 144 the countries instituted lockdown measures to curtail the virus and the second period is after 145 lockdown was in place. We obtained two different sets of parameters for some parameters in 146 each of the time periods; others remained the same, for instance the death rate, the disease 147 progression rate, the proportion of asymptomatic did not change over this time period. 148 The fitting was implemented using the standard nonlinear least squares approach with the Table 2 . The fitting for after lockdown for 152 UK is depicted in Figure 2 (b) and the estimated parameter values for the other countries 153 are given in Table 4 in Appendix A.

The numerical value of the reproduction number R 0 for United Kingdom before the country's 155 lockdown was put in place is estimated using the parameter values tabulated in Table 2 .

Consequently, using these parameter estimates, we obtain the value of R 0 for the COVID- is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint 

In order to carry our the sentiment analysis, tweets from Twitter were downloaded from 185 January 2, 2020 to May 29, 2020 for six countries, namely Australia, Brazil, Italy, South- factor driving the public sentiment but is being construed as fake news by some people.

In Brazil, the president accused the press of spreading panic and paranoia [12] , and called the virus "a small flu" and urged the people to go to the streets and "face the disease like We used the following procedure to generate sentiment scores for each country using COVID- is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. Post data collection, all tweets were translated to English using the googletrans package. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. ; a negative sentiment tweet, and > 0 as a positive sentiment tweet. The tweet scores are then averaged for a country per day. Finally, for each of the above listed countries, the 232 average positive sentiment per day was reported. Figure 5 shows the positive and negative 233 sentiments for the respective countries. To quantify the overall sentiment in each of the countries, we fitted straight lines (y p and y n 235 for positive and negative sentiments) through these sentiments; and we took the difference 236 of the lines y p and y n to determine if the overall sentiment from a country is positive or 237 negative during the time period the tweets were collected. We see in Figure 6 that Australia is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. ; https://doi.org/10.1101/2021.01.29.21250655 doi: medRxiv preprint Each of these six countries instituted lockdown measures as a way to control the spread of 249 the virus. We expect that as public awareness increases due to increased media coverage 250 of the infection and the lockdown mitigation efforts that public perception and sentiments 251 will be positive, therefore leading to a decrease in disease transmission. We therefore expect 252 the infection rate β to be a decreasing function of public sentiment. However, we see 253 from the sensitivity analysis that the infection rate β would increase the reproduction 254 number R 0 . Hence, we define a decreasing sentiment function for this parameter. We 255 also define a decreasing sentiment-related function for ν Q and ν H since these parameters 256 increases R 0 . However, the parameters ω Q and ω H are defined as increasing function of the 257 perception-related functions. We have chosen these parameters because these parameters 258 can be influenced by people's behavior, perceptions, and sentiments, unlike the recovery 259 rates, γ A , γ I , γ Q , γ H , death rates, δ A , δ I , δ Q , δ H , disease progression rate, and the proportion 260 asymptomatic, q. We discuss below how these functions are obtained for each of these is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint 

where β 0 , β 1 are the before and after lockdown infection rates. The variable C I is the cumulative number of symptomatic infectious individuals in the community; these are determined from the following equation.

Note that C I is not an epidemiological variable. Furthermore, m induces the effect of public 

Note that ν QM , ν HM , ω QM , ω HM > 0 for C I > 0. We assume that ν Q1 < ν Q0 , ν H1 < ν H0 , and ω Q1 > ω Q0 , ω H1 > ω H0 . Furthermore, for arbitrarily small number of symptomatic infectious individuals C I , the sentiment-related transition function ν QM converges to ν Q0 > 0 12 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity.

is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. ;

for small values of C I the maximum quarantine violation rate out of the quarantine class before the community lockdown. Also, as the cumulative number of infectious individuals C I grows, the quarantine violation function ν QM converges to ν Q1 , that is,

the minimum quarantine violation rate out of the quarantine class as public perceptions and 277 sentiments effects of the infection manifest in the community.

Similarly, the sentiment-related early hospital discharge rate, ν HM , from the hospitalized class, converges to ν H0 > 0, the maximum early discharge rate for small cumulative number of infectious individuals C I before the onset of public perceptions and sentiments about the disease, and lim Figure 8 : Simulation of the quarantine violation, e ν QM , and early hospital discharge, ν HM functions which incorporate public sentiments. Since ν Q and ν H increase R 0 , we used decreasing functions with sentiment that will reduce R 0 . Quarantine violation and early hospital discharge rate ν QM and ν HM , with the effect of public sentiments. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. Since ω Q and ω H decreases R 0 , we used increasing functions incorporating sentiments that will reduce R 0 . (a)-(b) Quaratine, ω QM , and hospitalization, ω HM functions with public sentiments.

The sentiment parameter m is expressed as m = 1 ε (y p + y n ), where y p is positive sentiments, 289 y n is negative sentiments, and ε is a scaling factor that scales the sentiments per 100,000 of 290 the population density. As described above, we fitted two straight lines through the positive 291 and negative sentiments for each of the countries (see Figure 5 ) to obtain the sentiment 292 variable y p and y n given as 293 y p = a p t + b p (5) y n = a n t + b n ,

where a p and a n are the slope of the straight lines and b p and b n are the intercept. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. ; https://doi.org/10.1101/2021.01.29.21250655 doi: medRxiv preprint

The reproduction number related to model (6) with Twitter sentiment is given as

where,

The reproduction number, R 0T , is the average number of secondary infectious produced 300 when a single infected individual is introduced into a completely susceptible population.

Next, we simulated the sentiment-related model (6) using the estimated parameters for each 302 country and plotted in Figure 10 is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. included in the model. We also see in Figure 11 (b) that negative public sentiments will yield 325 even more symptomatic infectious individuals in the population.

Thus, we see that it is important to incorporate public sentiment into epidemic models. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. and ω H ). We notice in Figure 12 is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. ;

and protestant groups, and the possible orgin of disinformation in the country. In Brazil, the prevalence of misinformation surrounding the pandemic is deeply concerning and many 370 people blame the messaging from the President Bolsonaro [37] .

To measure public sentiments across six countries across different geographical regions, we 372 downloaded tweets from the Twitter platform from January to May 2020. We then carried 373 out sentiment analysis that enabled us to separate the public sentiment into either positive 374 or negative sentiment. While our data set is a multilingual data set across multiple countries, on society than expected due to filter "bubbles" observed on Twitter [41] . Hence, it will 392 be beneficial to diversify the sources of public awareness and information in other to reach 393 many people as possible [41] and possibly reduce the spread of disinformation. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. ; vital to ensure public compliance and adherence with quarantine rules and all mitigation efforts (see 12). Doing so will go a long way in flattening the epidemic curve, and will lead to the kind of success story observed in New Zealand [65, 83] . 416 Our study demonstrated that the countries with positive sentiment, and quarantine compliance 417 have been more successful at curtailing the spread of the disease. In addition, we have 418 been able to demonstrate the impact on disease burden of early discharge of symptomatic 419 infectious individuals from hospital to make room for incoming sever COVID-19 patients. 420 Overall, our model is able to demonstrate the role of people's behavior and public sentiment 421 on disease transmission. Although, the trajectory of model simulation in Figure 10 (a) is able 422 to capture the trend of the actual trajectory of the cumulative number of cases in Figure   423 10(b), our simulation results saturate much earlier. A number of factors may be responsible 424 for this, which needs to be investigated in a future study.

Since we started this study, the number of cases in these countries has exploded, with is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted February 1, 2021. ;

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