Sage Journals: Discover world-class research

Abstract

The aim is to analyse that, during the current pandemic situation, the reduction in the number of cases of influenza suggests that the non-pharmaceutical interventions (NPIs) applied to contain the expansion of SARS-CoV-2 also affect the influenza expansion. We analyse the interaction of influenza and SARS-CoV-2 spread based on an extended SEIRD model for the Catalonia region in Spain. We show that the dynamic evolution of the spread of SARS-CoV-2 and influenza generates a small interference. This interference causes a small reduction in the number of cases of seasonal influenza, reducing its expansion over the population. Other elements like the face mask mandates, social distancing and hand cleaning boost the reduction in both expansions. Influenza expansion will present a small reduction in the number of cases due to the interaction with SARS-CoV-2 expansion but mainly because the NPIs applied to the population.

Keywords

Simulation optimization SARS-CoV-2 influenza interaction

Introduction

Along with the COVID-19 pandemic, caused by the SARS-CoV-2 expansion, the reduction in the number of cases of seasonal influenza is notorious, being this effect generalized in several countries.¹ The discussion of why this happens is relevant since it allows us to prepare the health system for possible increases and interactions between both viruses spread. In this study, we analyse the interaction between influenza and SARS-CoV-2 expansion using a model that represents this effect.

We consider influenza a stational disease² and COVID-19, at this point, not strongly influenced by climatic factors, with humidity as a key element as suggested in Tobías et al., Ward et al., Pineda Rojas et al., Mecenas et al., and Fontal et al.^3–7 The routes of transmission for influenza and SARS-CoV-2 seem to be a little different, being influenza is strongly transmitted by droplets,⁸ while SARS-CoV-2 also uses the airborne route of transmission.⁹ This has serious implications, as we can notice that the face mask will have a small effect on the containment of influenza^10,11 but strong effects with SARS-CoV-2^12–14 probably due to its airborne nature.¹⁵

The approach we follow is to use a modified SEIRD model that allows computing the interaction between the two spreads. We add to the model the possibility to represent a simple non-pharmaceutical intervention (NPI), the total lockdown. This will allow the validation of the model results with the observed pattern on the first waves analysed. We do our analysis for the Catalonia region.

There are several approaches to understanding the effects of NPIs on the population^16–20 in the context of the current COVID-19 pandemic. These analyses help in the validation process we do; however, they do not provide information regarding the effect that these NPIs can cause over other pandemics. Some works are analysing the interaction between SARS-CoV-2 and influenza over a population, like Domenech de Cellès et al.²¹ where the interaction to detect the effects of the coinfection over the increase of the SARS-CoV-2 transmission is analysed. In Dadashi et al.,²² the possibility of coinfection is analysed, which seems low, and in Stowe et al.,²³ it is analysed to detect the severity of this possible coinfection.

The paper is organized as follows: first, Section 2 presents the preliminary theoretical model we will use, and next, in Section 2.1, we present the model adaptation we will use for the representation of the interaction. This conceptual model represents the structural assumptions we will use in our model. Next, we present in Section 2.2 the model parametrization, which shows the data assumptions we will use, along with some simplification assumptions our model uses; the results for Catalonia are discussed in Section 3. Finally, in Section 4, some conclusions are pointed out.

Methods

The differences between both viruses are presented clearly on the parametrization of a classical SEIRD model²⁴ we can use to model the propagation of both viruses without any relation.

S^{'} = - \frac{β S I}{N},

(1)

E^{'} = \frac{β S I}{N} - α E,

(2)

I^{'} = α E - γ I,

(3)

R^{'} = γ (1 - μ) I,

(4)

D^{'} = γ μ I,

(5)

N = S + E + I + R + D .

(6)

The compartments S, E, I, R and D, are the susceptible, exposed, infective, recovered and dead sets, respectively. The latency rate (α) and recovery rate (γ) parameters will be considered constant, based on the measurements made by other studies, and N will be the total population of our analysis; in this case, we will be focused as a starting point, on the population in Catalonia, N = 7,653,845 at the time of this analysis.²⁵ We can assume that there is no pre-existing level of immunization to SARS-CoV-2 of influenza and that therefore the entire population is initially susceptible (S₀ = N). The fatality rate (µ) will be the fraction of sick people who do not recover. Thus, the crucial parameter to fit was the transmission rate (β), which we considered to be time-varying under the assumption of a step function. Each step would represent a government intervention (NPI, confinement, distribution of masks, reopening, etc.). We assumed that interventions are applied to control the disease, which will imply changes due to such interventions.²⁶

Adaptation of the SEIRD model, structural hypotheses used

Since we want to model the evolution of the interaction of two virus spreads, we expand the SEIRD model, see Figure 1, to be able to interact with a second SEIRD model that represents the spread of a second disease over the same population. In this case, we duplicate the compartments to consider the possibility of being susceptible or recovering from one of the two infections. The conceptualization of the model is presented in Figure 2. We have a Susceptible population, ‘S’, an exposed population to SARS-CoV-2, and ‘Es’, an exposed population to influenza as ‘Ei’, and then we have an infective population for SARS-CoV-2, ‘Is’, and for influenza, ‘Ii’, and recovered for SARS-CoV-2 as ‘Rs’ and for influenza as ‘Ri’. These last compartments Rs and Ri can be a starting point to becoming infected by the other virus.

Figure 1.

Classical compartments in a SEIRD model.

Figure 2.

The SEIRD model was adapted to contain the interaction between two viruses spread. In black, the main paths for a SARS-CoV-2 infection are presented, while in grey are for influenza infection.

The model implementation is done with InsightMaker a free tool under a General Public License (GPL adjusted) freely accessible through a browser.²⁷

The model presents some particularities that must be detailed. First, being influenzas a stationary pandemic, we must limit the β we use depending on the month. This is done in the variable seasonal effect, which represents a multiplier to influenza's β, that uses a function that represents a wave that oscillates from 0 to 1 and peaks in January, as is suggested by analysing the data for the influenza on the PIDIRAC service in Catalonia.²⁸ In the equations is represented as the season variable. The model does consider the possibility of reinfections for influenza and SARS-CoV-2 and considers the possibility of being infected with SARS-CoV-2 after an influenza infection or being infected with influenza after a SARS-CoV-2 infection. We do not also consider a simultaneous infection of both influenza and SARS-CoV-2. This is a conservative approach since seems that some type of cross-immunity exists, at least from the use of influenza vaccination^29–32 implying that the number of susceptible people will be higher on the model than the real value of the system. The equations that rule the model are derived from the basic equations of a SEIRD model combining both models and are presented next.

S^{'} = - ((I_{i} + I_{i_{2}}) β_{i} \frac{S}{N} S e a s o n + \frac{β_{s} S I_{s}}{N}) + w R_{i} + w R_{i_{2}} + w R_{s} + w R_{s_{2}},

(7)

E_{s}^{'} = \frac{β_{s} S (I_{s} + I_{s_{2}})}{N} - α_{s} E_{s},

(8)

I_{s}^{'} = α_{s} E_{s} - γ_{s} I_{s},

(9)

R_{s}^{'} = γ_{s} (1 - μ_{s}) I_{s} - (I_{i} + I_{i_{2}}) β_{i} \frac{R_{s}}{N} S e a s o n - w R_{s},

(10)

E_{i_{2}}^{'} = (I_{i} + I_{i_{2}}) β_{i} \frac{R_{s}}{N} S e a s o n - α_{i} E_{i 2},

(11)

I_{i_{2}}^{'} = α_{i} E_{i 2} - γ_{i} (1 - μ_{i}) I_{i_{2}} - γ_{i} μ_{i} I_{i_{2}},

(12)

R_{i_{2}}^{'} = γ_{i} (1 - μ_{i}) I_{i 2} - w R_{i_{2}},

(13)

D_{i}^{'} = γ_{i} μ_{i} (I_{i} + I_{i_{2}}),

(14)

E_{i}^{'} = (I_{i} + I_{i_{2}}) β_{i} \frac{S}{N} S e a s o n - α_{i} E_{i},

(15)

I_{i}^{'} = α_{i} E_{i} - γ_{i} I_{i},

(16)

R_{i}^{'} = γ_{i} (1 - μ_{i}) I_{i} - \frac{β_{s} R_{i} (I_{s} + I_{s_{2}})}{N} - w R_{i},

(17)

E_{S_{2}}^{'} = \frac{β_{s} R_{i} (I_{s} + I_{s_{2}})}{N} - α_{s} E_{s_{2}},

(18)

I_{S_{2}}^{'} = α_{s} E_{s_{2}} - γ_{S} (1 - μ_{S}) I_{S_{2}} - γ_{S} μ_{S} I_{S_{2}},

(19)

R_{S_{2}}^{'} = γ_{S} (1 - μ_{S}) I_{S_{2}} - w R_{s_{2}},

(20)

D_{s}^{'} = γ_{S} μ_{S} (I_{s} + I_{s_{2}}),

(21)

N = S + E_{i} + E_{i_{2}} + E_{s} + E_{s_{2}} + I_{i} + I_{i_{2}} + I_{s} + I_{s_{2}} + R_{i} + R_{i_{2}} + R_{s} + R_{s_{2}} + D_{i} + D_{s} .

(22)

Some simplification assumptions we made on the model are as follows:

The stationarity for SARS-CoV-2 is not as important as influenza, and although about 20% of the β can be due to stationarity on the model, we do not consider this for SARS-CoV-2 propagation; this will be interesting in case we want to study the stationary period after the initial spread of SARS-CoV-2.

We do not consider the possible waning protection of the vaccines that eventually increase the reinfections of SARS-CoV-2.

We do not consider the level of asymptomatic cases or the real number of cases for both propagations. This can have some effects at the end of a pandemic like COVID-19, where the system saturates, due to the reduction of people being infected, implying a higher value for beta instead of a low one, which causes the descent of the cases if the number of Susceptible people is still huge. This will imply that at the end of the Omicron wave, the per cent of reduction of the beta due to the measures will be small than the one represented in the model.

On the Python model used to estimate the β, we do not consider the deaths being an SEIR model; however, the resulting curves using those betas on the SEIRD model are coherent with the observed data.

We do not consider coinfection, which seems low.²²

We consider the population of Catalonia stable using the 2021 census.

In the next section, we detail the parametrization done for Catalonia, detailing the data hypotheses used in the model.

Model parametrization

Data assumptions are presented here. For SARS-CoV-2, the incubation time values are about 5.3³³ or 5.1,³⁴ the last value the one we will use. For the recovery period, we use 5 days.³⁵

The total lockdown in Catalonia takes place on 15 March 2020, but the effect on the curve happens on 21 March 2020. This will be the value we will use to change the β for the propagation due to the NPI application. The initial value for the SARS-CoV-2 β is 1.23 and with the application of the measures is reduced to 0.17, representing about 13%. We assume that these measures also affect the reduction of influenza transmission, being the lockdowns, recommendations for hand cleaning, face mask use and social distancing measures that also affect influenza transmission.¹¹ We assume a similar reduction for influenza β, 13% of its original value.

On the model, it is also needed to establish the first case for SARS-CoV-2, being this relevant to detail the β to be used in its expansion. This, however, will not be relevant to understanding the interaction, since as we will see, the key aspect is the fact that the β of influenza is lower than the β for SARS-CoV-2. The first SARS-CoV-2 reported case in Catalonia is due to an Italian woman that go to a hospital because presented symptoms on 20 February 2020,³⁶ hence being the incubation of about 5 days the first ‘exposed’ case take place on 15 February 2020, being this the day we use to start our propagation for SARS-CoV-2 for Catalonia case.

For the calculus of the β, we use a Python optimization model^37,38 that uses the same start day but that calculates, using an optimization algorithm, the values for the different β resulting from the application of the different NPIs over the population. In Table 1, we can see the β values for the different turning points (NPIs) in Catalonia. The code can be found in Online Appendix 1.

Table 1.

Turning points and values for the β of the model considering the NPIs applied over the population.

Turning points	Date	Day on model	≈NPI date^a	β		Description event
1	15 Feb 20	1140		1.23	100	First case
2	21 Mar 20	1175	15 Mar 20	0.17	13.762215	Total confinement
3	26 Jun 20	1272	18 Jun 20	0.35	28.7459283	New normality
4	19 Jul 20	1295	16 Jul 20	0.2	16.5309446	Summer contention
2	29 Sep 20	1367	15 Sep 20	0.31	25.3257329	School returns
6	26 Oct 20	1394	20 Oct 20 and 25 Oct 20	0.14	11.4820847	2nd wave contention (increase teleducation and teleworking)
7	2 Feb 20	1431	23 Nov 20	0.27	21.5798046	Reopen bars
8	16 Jan 21	1476	02 Jan 21 and 11 Jan 21	0.16	13.1921824	Start of vaccination and contention 3rd wave
9	8 Mar 21	1527	09 Feb 21 and 22 Feb 21	0.22	17.5895765	Relaxation of measures
10	25 Apr21	1575	Vaccination process	0.15	12.4592834	Vaccine's effect
11	12 Jun 21	1623	7 Jun 21	0.5	40.3908795	Social reopening (Delta)
12	10 Jul 21	1651	9 Jul 21	0.13	10.6677524	5th wave contention
13	7 Oct 21	1740	1 Oct 21 and 15 Oct 21	0.33	26.8729642	Detection increase and social reopening
14	12 Nov 21	1776	12 Nov 21	0.34	27.52443	Omicron
15	19 Jan 22	1844		0.11	9.28338762

The dates include the delay until the effect of the NPI is applied, hence must include the incubation period and the notification period.

Abbreviation: NPI: non-pharmaceutical intervention.

Figure 3 shows the SARS-CoV-2 waves in Catalonia due to the different NPIs application that results in different regimes for the curve (different β).

Figure 3.

Optimization model to fit the transmission rate for the SARS-CoV-2 in Catalonia, from February 2020 to April 2022.

Figure 4.

Comparison of influenza spread and model spread in Catalonia. Left: influenza cases for the 2018–2019 campaign in Catalonia: right: influenza cases for the 2019–2020 campaign in Catalonia. Source: Torner et al.⁴¹ ‘VG’ refers to the genetic variant, ‘nivell basal’ is the baseline level, ‘nivell epidemic’ is the epidemic level with moderate level ‘nivell moderat’, high level ‘nivell alt’, and very high level ‘nivell molt alt’.

The calculated β for the first wave is 1.23 until the lockdown where it is 0.17; using the expression R₀ = β/γ, we can obtain a value for R₀ of 6.27. This value is coherent with the values proposed for R₀, of about 3.38 ± 1.40, with a range of 1.90 to 6.49,³⁹ or the values that are calculated on López L and Rodó²⁰ for Catalonia. Notice that we are focused on the first wave in Catalonia; hence, we are not considering other variants like Delta or Omicron that seem to increase this value.^39,40

The model will start on 01 January 2017, to perform stabilization of the influenza propagation dynamic; Week 40 of 2019 is the first week that we must use for the validation with the data from the PIDIRAC service in Catalonia.²⁸ We use the reports for 2018–2019, 2019–2020 (the start of the COVID-19 pandemic) and 2020–2021 (during the COVID-19 pandemic); see Torner et al. and de Catalunya and de Salut.^41–43 This last report for 2021–2022 showed that a small number of influenza cases in Catalonia are detected.

To be consistent with the historical values obtained by the epidemiological service in Catalonia for the 2018–2019 and 2019–2020 campaigns,⁴¹ influenza spread in Catalonia must be about β = 0.36, see Figure 4. Therefore, for influenza, the parameter we will use as R₀ is 1.85, which is in the range of the values proposed in Biggerstaff et al.⁴⁴ Furthermore, we must keep a basal level of influenzas cases of 15, being this coherent with the information presented by the PIDIRAC.²⁸ For influenza, the incubation is estimated with a mean of 2 days,⁴⁵ while the infective period is about 5–7 days⁴⁶; we will use 5.

With this value, we obtain a curve with a maximum of about 350 cases for 100K people (27K for all the Catalonia population) that is coherent with the observed data for the seasonal influenza wave in Catalonia for the 2018–2019 and 2019–2020 seasons (see Figure 5); the values obtained with the model fits well with the observed ones.

Figure 5.

Scenario 03: application of the NPIs over SARS-CoV-2 but considering that they do not have any effect on influenza spread. Notice that seasonal influenza is affected but not at the level we observed in those years.

The protection offered by a natural influenza infection is under discussion, although some analysis shows that the protection for a specific variant last for a long,⁴⁷ some other analysts suggest that reinfection with the same variant is not rare and can happen in a year.⁴⁸ In existing different variants, we assume in our model that the reinfection of influenza can be done in a year.

The protection for SARS-CoV-2 reinfection depends on the vaccination process and the protection due to the natural infection.

Summarizing all this, data assumptions that represent the model parametrization are presented in Table 2.

Table 2.

Parameters for the SEIRD models to be used in the analysis on Catalonia.

Symbol	Meaning	SARS-CoV-2 value (days)	Influenza value
α	Latency (incubation) period	5.1 ³⁴ −4 (Delta) 3 (Omicron)	2 ⁴⁵
γ	Recovery (infective) period	5 ³⁵	5 ⁴⁶
N	Total population	7,653,845 ²⁵	7,653,845
µ	Fatality rate	0.002 ⁴⁹	0.000018 ⁴⁹
β	Transmission rate	1.259^a	0.36 ⁴⁴
w	Immunity waning	1/180 days	1/365 days

SARS-CoV-2 will change depending on the variants and the NPIs actions to be applied.

Abbreviation: NPI: non-pharmaceutical intervention.

Results

We conduct different scenarios with the model that analysed the interaction of SARS-CoV-2 and influenza over the effects of the different NPIs applied to the population. Notice that the last β we will use in the SARS-CoV-2 model is about 0.11, to represent the descent in the number of cases. This value, however, is not representing the application of any NPIs but just a natural decrease in the number of cases due to the saturation of the system and because of the under detection due to the high number of asymptomatic cases. Asymptomatic has an estimation of about 40%⁵⁰ increasing to almost 70% for Omicron.⁵¹ This implies that mainly the NPIs that remain are the face mask in interiors, allowing us to evaluate the effect of this NPI over the influenza spread, understanding that other NPI that remain at this point are not mandatory. The results of the scenarios are presented in the next figures. The initial date (01 January 2017) is Day 0, and the date of the first COVID-19 case is Day 1140 (15 February 2020); on the figures, the y-axis represents the simulation day, and to simplify the understanding, we add, in Table 3, the relation between the simulation day and the date; also, on the figures, the years until 2025 are added.

Table 3.

Relation of the simulation day with the dates.

Data	Day	Comment
1 Jan 17	0	Start of the simulation
1 Jan 18	365
1 Jan 19	730
1 Jan 20	1095
15 Feb 20	1140	First COVID-19 case
1 Jan 21	1461
1 Jan 22	1826
1 Jan 23	2191
1 Jan 24	2556
1 Jan 25	2922

Discussion

Scenario 01 and Scenario 02 (Figures 6 and 7) present two situations mainly for the validation of the model. Figure 6 shows the normal regime of the seasonal influenzas under normal circumstances, with no COVID-19 pandemic, and the first 3 years are for the stabilization of the model. Figure 7 presents a hypothetical scenario where no NPIs have been applied to the population. This last scenario shows a plausible end situation for the pandemic, where no reduction in the protection due to natural immunity happens and no new variants appear. Notice the long downtrend of the SARS-CoV-2 cases.

Figure 6.

Scenario 01: no COVID-19 pandemic. With a TR of 0 for SARS-CoV-2, this scenario is for the validation of the stationary behaviour of seasonal influenza in Catalonia. The first 3 years are for the stabilization of the model.

Figure 7.

Scenario 02: no application of any NPI over the SARS-CoV-2. To detect if influenza spread will be affected only because of the interaction with SARS-CoV-2. NPI: non-pharmaceutical intervention.

Scenario 03 and Scenario 04, see Figures 5 and 8, show two plausible situations. In both cases, we can see a reduction in the number of cases of influenza due to the interaction. In the case that the NPIs do not affect influenza spread, the reduction in the waves during the COVID-19 pandemic is from 27K cases in January 2020 to 21K cases in January 2021 and 19K cases in January 2022. These values are in contradiction with what we observed in Catalonia during those years; hence we can consider that there are other elements, the NPIs applied over the population, and not only the interaction. A plausible explanation for this reduction is because SARS-CoV-2 sick people are going to become aisled, they will not be infected by influenza, being the routes of transmission of influenza included the routes of transmission of SARS-CoV-2. Therefore, some NPIs that clearly will have an important effect on the containment of both spreads are the confinements of the positives and close contact over almost 15 days (about 2 weeks). This can have a noticeable effect on the control of both diseases since the susceptible population reduces drastically. This NPI is included in the reduction of the β for the SARS-CoV-2 spread but is not analysed in isolated.

All these scenarios suggest that, although the interaction between SARS-CoV-2 and influenza exists, the NPIs play a key role in the control of both spreads, coherently with current results.^52,53

Scenario 05, see Figure 9, defines a situation where the remaining NPIs, indoor face mask use, remain, suggesting that face masks have some kind of effect also in the control of influenza. This is providing evidence in the opposite sense^10,11 but coherent with the analysis done due to the specific situation generated by the SARS-CoV-2 spread,^12–14 suggesting that the wide use of face mask has some effect on the containment of the spread of other respiratory viruses, not only for COVID-19 prevention. Coherently with this, countries with the widespread use of face masks, like Japan,^54–56 present low levels of cases in the common influenza seasons. Specifically, we observed an incidence of 350 cases for 100K habitats in Catalonia to about 214 cases for 100K habitats in Japan,⁵⁷ representing a reduction of about 61%. However, this reduction cannot be entirely attributed to the use of masks, as other unanalysed factors could also cause this reduction, such as cultural or technological ones.

Being the route of transmission similar to influenzas and SARS-CoV-2 (but not equal), it is reasonable to consider that these NPIs also have effects on the influenza contention, hence reducing its transmission. In case no NPIs have been applied to the population, the resulting interference between both spreads ends in a small reduction in the number of influenza cases.

The model can be used to analyse and control a syndemic, a synergistic epidemic that is composed of the combination of two or more concurrent or also sequential epidemics, like in the case of influenza and COVID-19. This concurrent or sequential epidemic happens over the same population causing interactions. Each one of the epidemics analysed can cause an increase in the number of cases that needs medical attention. The increase in the number of cases the health service must attend can cause a decrease in the quality of the service or, in the worst case, a collapse of the health service; this implies an obvious worsening of the prognosis of both diseases. Understanding the interaction of the two expansions can help in making the right decisions to reduce the transmission and also can help to understand the scenarios we face in case the NPIs do not work to control the transmission of the different pandemics analysed.

Although this model is focused, for validation purposes on Catalonia, we can infer that this pattern can be applied to other countries and that this interference appears always when we have two waves that use similar transmission paths.

Figure 8.

Scenario 04: application of the NPIs over SARS-CoV-2 and considering that they also affect seasonal influenza. This scenario allows seeing if influenza spread will be affected because of the interaction with SARS-CoV-2 and the NPI application. This scenario considers that the effects of the last NPI remain active affecting both influenza and SARS-CoV-2. NPI: non-pharmaceutical intervention.

Figure 9.

Scenario 05 considers that just the last NPIs that remain in Catalonia (indoor face mask mandates and the possible new behaviours adopted by the population) do not affect influenza spread. Notice that the influenza wave of 2022 does not happen; therefore, the NPIs also affect influenza spread. NPIs: non-pharmaceutical interventions.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Ethical approval statement

No experiment involving animals or persons has been conducted. All the data used can be freely accessible.

ORCID iD

Pau Fonseca i Casas

References

Olsen

Azziz-Baumgartner

Budd

, et al. Decreased influenza activity during the COVID-19 pandemic — United States, Australia, Chile, and South Africa, 2020. MMWR Morb Mortal Wkly Rep [Internet] 2020 [cited 2022 Mar 11]; 69: 1305–1309. https://www.cdc.gov/mmwr/volumes/69/wr/mm6937a6.htm.

Lowen

Mubareka

Steel

, et al. Influenza virus transmission is dependent on relative humidity and temperature. PLoS Pathog 2007; 3: 1470–1476.

Tobías

Molina

Rodrigo

, et al. Meteorological factors and incidence of COVID-19 during the first wave of the pandemic in Catalonia (Spain): a multi-county study. One Heal 2021; 12: 100239–100246.

Ward

Xiao

Zhang

. Humidity is a consistent climatic factor contributing to SARS-CoV-2 transmission. Transbound Emerg Dis 2020; 67: 3069–3074.

Pineda Rojas

Cordo

Saurral

, et al. Relative humidity predicts day-to-day variations in COVID-19 cases in the city of Buenos Aires. Environ Sci Technol 2021; 55: 11176–11182.

Mecenas

da Rosa Moreira Bastos

Rosário Vallinoto

, et al. Effects of temperature and humidity on the spread of COVID-19: a systematic review. PLoS One 2020; 15: 1–21.

Fontal

Bouma

San-José

, et al. Climatic signatures in the different COVID-19 pandemic waves across both hemispheres. Nat Comput Sci 2021; 1: 655–665.

Killingley

Bennett

Van-Tam

. Routes of transmission of the influenza virus scientific evidence base review. 2010.

Morawska

Cao

. Airborne transmission of SARS-CoV-2: the world should face the reality. Environ Int [Internet] 2020; 139: 105730. https://doi.org/10.1016/j.envint.2020.105730.

10.

Long

Liu

, et al. Effectiveness of N95 respirators versus surgical masks against influenza: a systematic review and meta-analysis. J Evid Based Med [Internet] 2020 [cited 2022 Jan 25]; 13: 93–101. https://pubmed.ncbi.nlm.nih.gov/32167245/.

11.

Jefferson

Del Mar

Dooley

, et al. Physical interventions to interrupt or reduce the spread of respiratory viruses. Cochrane Database Syst Rev [Internet] 2020 [cited 2022 Jan 25]; 2020. https://pubmed.ncbi.nlm.nih.gov/21735402/.

12.

Howard

Huang

, et al. An evidence review of face masks against COVID-19. Proc Natl Acad Sci [Internet] 2021 [cited 2022 Jan 23]; 118: e2014564118. https://www.pnas.org/content/118/4/e2014564118.

13.

Tabatabaeizadeh

S-A

. Airborne transmission of COVID-19 and the role of face mask to prevent it: a systematic review and meta-analysis. Eur J Med Res [Internet] 2021 [cited 2022 Jan 25]; 26: 1. https://pubmed.ncbi.nlm.nih.gov/33388089/.

14.

Chu

Akl

Duda

, et al. Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: a systematic review and meta-analysis. Lancet [Internet] 2020; 395: 1973–1987. https://linkinghub.elsevier.com/retrieve/pii/S0140673620311429.

15.

Zhang

, et al. Identifying airborne transmission as the dominant route for the spread of COVID-19. Proc Natl Acad Sci U S A 2020; 117: 14857–14863.

16.

Bpt

Mbchb

, et al. The temporal association of introducing and lifting non-pharmaceutical interventions with the time-varying reproduction number (R) of SARS-CoV-2: a modelling study across 131 countries. Lancet Infect Dis [Internet] 2020; 0. www.thelancet.com/infection.

17.

Brauner

Mindermann

Sharma

, et al. Inferring the effectiveness of government interventions against COVID-19. Science (80-) [Internet] 2020; 9338: eabd9338. https://www.sciencemag.org/lookup/doi/10.1126/science.abd9338.

18.

Haug

Geyrhofer

Londei

, et al. Ranking the effectiveness of worldwide COVID-19 government interventions. Nat Hum Behav 2020; 4: 1303–1312.

19.

Matzinger

Skinner

. Strong impact of closing schools, closing bars and wearing masks during the Covid-19 pandemic: results from a simple and revealing analysis. medRxiv [Internet]. 2020;2020.09.26.20202457, http://medrxiv.org/content/early/2020/09/28/2020.09.26.20202457.abstract.

20.

López

Rodó

. A modified SEIR model to predict the COVID-19 outbreak in Spain and Italy: simulating control scenarios and multi-scale epidemics. Results Phys 2021; 21: 103746.

21.

Domenech de Cellès

Casalegno

J-S

Lina

, et al. Estimating the impact of influenza on the epidemiological dynamics of SARS-CoV-2. PeerJ [Internet] 2021 [cited 2023 Mar 16]; 9: e12566. https://peerj.com/articles/12566.

22.

Dadashi

Khaleghnejad

Abedi Elkhichi

, et al. COVID-19 and influenza co-infection: a systematic review and meta-analysis. Front Med (Lausanne) [Internet] 2021 [cited 2023 Mar 16]; 8. https://pubmed.ncbi.nlm.nih.gov/34249971/.

23.

Stowe

Tessier

Zhao

, et al. Interactions between SARS-CoV-2 and influenza, and the impact of coinfection on disease severity: a test-negative design. Int J Epidemiol [Internet] 2021 [cited 2023 Mar 16]; 50: 1124–1133. /pmc/articles/PMC8135706/.

24.

Vynnycky

White

. An introduction to infectious disease modelling. New York, NY, USA: Oxford University Press, 2010.

25.

Servei Català de la Salut and Generalitat de Catalunya . Població de referència del Servei Català de la Salut per a l’any Dades per ABS i UP assignada [Internet]. [cited 2022 Feb 13], https://catsalut.gencat.cat/web/.content/minisite/catsalut/proveidors_professionals/registres_catalegs/documents/poblacio-referencia.pdf (2020).

26.

Dehning

Zierenberg

Spitzner

, et al. Inferring change points in the spread of COVID-19 reveals the effectiveness of interventions. Science (80-) [Internet] 2020; 9789: eabb9789. https://www.sciencemag.org/lookup/doi/10.1126/science.abb9789.

27.

Fonseca i Casas

Garcia i Carrasco

Garcia I Subirana

. Influenza vs SARS-CoV-2 | Insight Maker [Internet]. InsightMaker. [cited 2022 Feb 19], https://insightmaker.com/insight/5HY9AzDKzQQABD3Rx9nKZb/Influenza-vs-SARS-CoV-2 (2022).

28.

Departament de Salut de Catalunya. Pla d’informació de les infeccions respiratòries agudes a Catalunya (PIDIRAC). Canal Salut [Internet]. Pla d’informació de les infeccions respiratòries agudes a Catalunya (PIDIRAC). [cited 2022 Mar 12], https://canalsalut.gencat.cat/ca/professionals/vigilancia-epidemiologica/pla-dinformacio-de-les-infeccions-respiratories-agudes-a-catalunya-pidirac/ (2021).

29.

Reche

. Potential cross-reactive immunity to SARS-CoV-2 from common human pathogens and vaccines. Front Immunol [Internet] 2020 [cited 2022 Feb 10]; 11. https://pubmed.ncbi.nlm.nih.gov/33178220/.

30.

Green

Ashkenazi

Merzon

, et al. The association of previous influenza vaccination and coronavirus disease-2019. Hum Vaccin Immunother [Internet] 2021 [cited 2022 Feb 10]; 17: 2169–2175. https://pubmed.ncbi.nlm.nih.gov/33377817/.

31.

Greco

Cucci

Portulano

, et al. Effects of influenza vaccination on the response to BNT162b2 messenger RNA COVID-19 vaccine in healthcare workers. J Clin Med Res [Internet] 2021; 13: 549–555. http://www.jocmr.org/index.php/JOCMR/article/view/4590.

32.

Dangi

Palacio

Sanchez

, et al. Cross-protective immunity following coronavirus vaccination and coronavirus infection. J Clin Invest [Internet] 2021 [cited 2022 Mar 15]; 131. https://doi.org/10.1172/JCI151969DS1

33.

Pak

Langohr

Ning

, et al. Modeling the coronavirus disease 2019 incubation period: impact on quarantine policy. Mathematics 2020; 8: 1631–1639. https://doi.org/10.3390/math8091631

34.

Lauer

Grantz

, et al. The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: estimation and application. Ann Intern Med 2020; 2019: 577–582.

35.

Lin

Zhao

Gao

, et al. A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action. Int J Infect Dis [Internet] 2020; 93: 211–216. https://doi.org/10.1016/j.ijid.2020.02.058.

36.

ASPCAT. Una italiana resident a Barcelona, primer cas per coronavirus a Catalunya. Agència de Salut Pública de Catalunya (ASPCAT) [Internet]. [cited 2022 Feb 16], https://salutpublica.gencat.cat/ca/detalls/Article/Una-italiana-resident-a-Barcelona-primer-cas-de-coronavirus-a-Catalunya (2020).

37.

Fonseca i Casas

García i Carrasco

Garcia i Subirana

. SEIRD COVID-19 formal characterization and model comparison validation. Appl Sci [Internet] 2020; 10: 5162. https://www.mdpi.com/2076-3417/10/15/5162.

38.

Fonseca I Casas

Garcia I Subirana

García I Carrasco

, et al. Sars-cov-2 spread forecast dynamic model validation thorough digital twin approach, catalonia case study. Mathematics 2021; 9: 1–17.

39.

Alimohamadi

Taghdir

Sepandi

. Estimate of the basic reproduction number for COVID-19: a systematic review and meta-analysis. J Prev Med Public Heal [Internet] 2020 [cited 2022 Feb 8]; 53: 151–157. https://pubmed.ncbi.nlm.nih.gov/32498136/.

40.

Ito

Piantham

Nishiura

. Relative instantaneous reproduction number of Omicron SARS-CoV-2 variant with respect to the Delta variant in Denmark. J Med Virol [Internet] 2022 [cited 2022 Feb 8]; 94: 2265–2268. https://pubmed.ncbi.nlm.nih.gov/34967453/.

41.

Torner

Basile

Martínez

. Balanç temporada gripal 2018-2019 [Internet]. [cited 2022 Jan 13], http://canalsalut.gencat.cat/ca/professionals/vigilancia-epidemiologica/pla- (2019).

42.

de Catalunya

de Salut

. Balanç temporada gripal 2019-2020 [Internet]. Pla d’informació de les infeccions respiratòries agudes a Catalunya. [cited 2022 Mar 12], https://canalsalut.gencat.cat/web/.content/_Professionals/Vigilancia_epidemiologica/documents/arxius/balanc-temporada-gripal-2019-20.pdf (2020).

43.

de Catalunya

de Salut

. Balanç del programa PIDIRAC 2020-2021 [Internet]. [cited 2022 Mar 12], https://canalsalut.gencat.cat/web/.content/_Professionals/Vigilancia_epidemiologica/documents/arxius/Balanc-PIDIRAC-20-21-V2.pdf (2021).

44.

Biggerstaff

Cauchemez

Reed

, et al. Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature. BMC Infect Dis [Internet] 2014 [cited 2022 Feb 17]; 14: 480. https://bmcinfectdis.biomedcentral.com/articles/10.1186/1471-2334-14-480.

45.

Schmitt

. Influenza, seasonal. In: My child is sick! 2nd ed. [Internet]. American Academy of Pediatrics, 2016 [cited 2022 Feb 16]. pp. 195–205. https://www.who.int/news-room/fact-sheets/detail/influenza-(seasonal).

46.

CDC - Centers for Disease Control and Prevention. How Flu Spreads | CDC [Internet]. [cited 2022 Feb 17], https://www.cdc.gov/flu/about/disease/spread.htm (2018).

47.

Krammer

. The human antibody response to influenza A virus infection and vaccination. Nat Rev Immunol [Internet] 2019 [cited 2022 Mar 15]; 19: 383–397. https://www.nature.com/articles/s41577-019-0143-6.

48.

Memoli

Han

Walters

, et al. Influenza A reinfection in sequential human challenge: implications for protective immunity and “universal” vaccine development. Clin Infect Dis [Internet] 2020 [cited 2022 Mar 15]; 70: 748–753. https://academic.oup.com/cid/article/70/5/748/5429562.

49.

Iacobucci

. COVID and flu: what do the numbers tell us about morbidity and deaths? Br Med J [Internet] 2021 [cited 2022 Feb 18]; 375: n2514. https://www.bmj.com/content/375/bmj.n2514.

50.

Liu

, et al. Global percentage of asymptomatic SARS-CoV-2 infections among the tested population and individuals with confirmed COVID-19 diagnosis. JAMA Netw Open [Internet] 2021 [cited 2022 Feb 5]; 4: e2137257. https://jamanetwork.com/journals/jamanetworkopen/fullarticle/2787098.

51.

Yifei

Zhang

, et al. Proportion of asymptomatic infection and nonsevere disease caused by SARS-CoV-2 Omicron variant: a systematic review and analysis. J Med Virol 2022; 94: 5790–5801. https://doi.org/10.1002/jmv.28066

52.

Paget

Caini

Del Riccio

, et al.

Has influenza B/Yamagata become extinct and what implications might this have for quadrivalent influenza vaccines?

Eurosurveillance [Internet] 2022 [cited 2022 Nov 14]; 27: 2200753. https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2022.27.39.2200753.

53.

Chen

Lourenço

, et al. Measuring the effects of COVID-19-related disruption on dengue transmission in Southeast Asia and Latin America: a statistical modelling study. Lancet Infect Dis [Internet] 2022 [cited 2022 Nov 14]; 22: 657–667. http://www.thelancet.com/article/S1473309922000251/fulltext.

54.

Nakayachi

Ozaki

Shibata

, et al.

Why do Japanese people use masks against COVID-19, even though masks are unlikely to offer protection from infection?

Front Psychol 2020; 11: 1918.

55.

Burgess

Horii

. Risk, ritual and health responsibilisation: Japan’s ‘safety blanket’ of surgical face mask-wearing. Sociol Health Illn [Internet] 2012 [cited 2022 Apr 6]; 34: 1184–1198. https://onlinelibrary.wiley.com/doi/full/10.1111/j.1467-9566.2012.01466.x.

56.

Machida

Nakamura

Saito

, et al. Incorrect use of face masks during the current COVID-19 pandemic among the general public in Japan. Int J Environ Res Public Health [Internet] 2020 [cited 2022 Apr 6]; 17: 1–11. /pmc/articles/PMC7557398/.

57.

Nippon.com. Flu cases in Japan remain extremely low again in 2021–22 | Nippon.com [Internet]. nippon.com. [cited 2022 Apr 4], https://www.nippon.com/en/japan-data/h01219/ (2022).

Modelling influenza and SARS-CoV-2 interaction: Analysis for Catalonia region

Abstract

Keywords

Introduction

Methods

Adaptation of the SEIRD model, structural hypotheses used

Model parametrization

Results

Discussion

Footnotes

Declaration of conflicting interests

Funding

Ethical approval statement

ORCID iD

References