Estimating COVID-19 cases and reproduction number in Mexico (working paper)

In this report we fit the semi-mechanistic Bayesian hierarchical model found in [1, 2] to describe the Mexican COVID-19 epidemic. We obtain two epidemiological measures: the number of infections and the reproduction number. The modelling framework requires sufficient death data to estimate trends. Therefore, we limit the analysis to states that have a total of more than a hundred deaths. We expect our estimates to be more accurate than the attack rates estimated from the reported number of cases.

1 Introduction

As of today, there are more than 6 million of confirmed cases of coronavirus disease 2019 (COVID-19) in the world, and a total of 372,344 reported deaths [3]. Mexico has 87,512 COVID-19 confirmed cases with 9,779 deaths. The numbers are growing rapidly in the country, along with plans for a gradual reopening starting in June. In addition to this, the testing rate in Mexico is the lowest among the OECD countries, implying a likely large subreporting of cases. The health system has started to overload in Mexico City and other high population centers. Given this, a better understanding of the current epidemiological situation at the state level, and the impact of government-imposed mitigation measures is necessary. Here, we use a semi-mechanistic Bayesian hierarchical model of COVID-19 epidemiological dynamics [1, 2] to assess the effect of different control interventions in Mexico. We estimate the number of infections and the time-varying reproduction number as a function of human mobility.

Below we have the map of cases (a) and deaths (b) in Mexico by state level. Data source, accessed on May 28, 2020.

The distribution of deaths among states is highly heterogeneous, with 3 states, Mexico City, State of Mexico, and Baja California, accounting for almost half of the deaths reported to date.

Mexico’s government determined three phases of contingency for the COVID-19 pandemic. The first two cases were confirmed on February 27, from travellers returning from Italy to Sinaloa and Mexico City. Later, on March 17, the suspension of school activities began nationally. A week later, on March 23, The Comité Nacional para la Seguridad en Salud announced the start of the second phase of the epidemic. Almost a month later, on April 21, phase three was declared. Distancing measures included suspension of all non essential activities of public, private and social sectors. The measures were initially planned to last until April 30, but were later extended until May 17 or May 30, depending on the local situation of every municipality of the country. It remains unclear the extent to which these measures have been effective in reducing transmission across the country. Reported cases are growing fast and show little sign of slowing. Given this rapid growth, a better understanding of the current situation and the impact of interventions deployed to date is required to guide policy decisions.

2 Assumptions

Next we explain some important assumptions made within our modelling framework. To estimate \(R_t\), the time-varying effective reproduction number across all states, we parameterised \(R_t\) as a function of Google mobility data, as adopted in [2]. Also, the onset-to-death distribution and estimates of the virus transmissibility (the basic reproduction number, \(R_0\)) are considered as in [2].

Now, in Mexico, there are two evident and significant problems that must be considered with death data. One of them is the death-delayed reporting [4], and the other is the underreporting. The death-delayed reporting refers to COVID-19 deaths that will take time to report. Death records must be validated by two information systems, which obtain information from medical units and health jurisdictions. Many of the COVID-19 deaths that were tested are awaiting the proper certification and classification. The assessment and confirmation processes take days. That is why the official figures of deaths from COVID-19, published by the Ministry of Health, have an important lag. The plot below illustrates the cumulative proportion of deaths reported as the delay increases, with different colours corresponding to different dates of death. Very few deaths (around 10%) are reported within one day, and the vast majority of deaths (around 90%) are reported after three weeks.

We are dividing the case numbers of each day by our proportion of cases reported estimates, that we computed with the empirical distribution. We do not report the last two days, since underreporting in those two days is very high. Also, we assume the delay has the same distribution in all the country, but this can be corrected when more data becomes available. Even more, we assume that the delay distribution does not change in time. We plan to add a weekly cycle in the reporting delay, but the distribution may also move in time affected by the load on the system.

The underreporting refers to COVID-19 deaths that will not be reported. Estimating the extent of the underreporting remains very difficult, especially in areas outside of Mexico City where studies have not been conducted. Estimates of excess deaths can provide information about the burden of mortality potentially related to the COVID-19 pandemic, including deaths that are directly or indirectly attributed to COVID-19. However, in Mexico, there are no official published data on deaths during 2020. The publication of death statistics is annual and the last record is from the year 2018. In Mexico City, there are several death certificates stating that the confirmed or probable cause of death was COVID-19, three times higher than the COVID-19 deaths reported by the government [5]. Another study of the death certificates shows that the excess mortality derived from the COVID-19 health crisis in Mexico City is four times greater than that reported [6]. This excess includes both people who died from COVID-19 and also those who died from other causes derived from the health crisis.

We adopted the extension of the semi-mechanistic Bayesian hierarchical model from [2] to reflect the uncertainty about underreported deaths. Meaning that we address the effect of underreporting in the data by setting a \(\psi \sim beta(\theta, \rho)\) prior distribution to death underreporting, where both of the hyperparameters of the beta density are fixed in 30, in order to get a mode of 50%. Below appears the plot of this prior distribution.

Although the underreporting rate could be different in each state of the country, for now, there are no data to define a prior distribution to death underreporting for each state.

Lastly, there is uncertainty surrounding the state-level Infection Fatality Ratio (IFR), which is the ratio of deaths divided by the number of actual infections. Estimates of the expected IFR across different states are derived from the previously published estimates that appear on [2] for the cities of São Paulo and Maranhão with the following procedure: We consider the IFR of Mexico City as the IFR of São Paulo, and the IFR of Chiapas and Oaxaca, which are the most marginalized states in Mexico, equivalent to Maranhão. Then, we weight according to age groups. Finally, we interpolated the rest of the states using five levels of the CONAPO state marginalization index. With this, we are accounting for the substantial heterogeneity we expect to observe in health outcomes across states, due to variation in healthcare quality and capacity. The marginalization index is an official standard indicator that allows states to be differentiated according to the deprivations suffered by the population, such as education, housing, monetary income, or access to health services.

3 Data

As input of deaths and reported cases, our model uses daily updates from the Dirección General de Epidemiología , and the historical bases on cases associated with COVID-19 nationwide (accessed on 2020-05-20).

For population counts we used two measures. To compute the attack rates and estimate the reproduction numbers we use the Consejo Nacional de Población (CONAPO) population projections for 2020, accessed on 2020-05-27 from here and here. The projections are not disaggregated for the age groups over 65 years old. Therefore, for the IFRs computations, we used the Instituto Nacional de Estadística y Geografía (INEGI) 2015 intercensal survey (downloaded in 2020-05-30).

Regarding intervention data, the values taken into account are the dates in which interventions were effectively applied, even though they were encouraged at earlier dates.

4 Results

The attack rate (AR) is the proportion of individuals within each state that has been infected to date. The following table shows the estimated IFR, state population, reported deaths and deaths per million population, estimated number of infections in thousands, and estimated AR.

State	IFR %	Population	Deaths	Deaths per million	Infections (thousands)	Attack rate %
Mexico City	0.59	9018645	2115	235.0	1540 [1360,1690]	17.1 [15,18.8]
State of Mexico	0.53	17427790	1516	87.0	1100 [956,1210]	6.3 [5.5,7]
Baja California	0.36	3634868	812	223.0	845 [741,932]	23.2 [20.4,25.6]
Veracruz	0.97	8539862	509	59.6	453 [385,507]	5.3 [4.5,5.9]
Tabasco	0.71	2572287	483	188.0	304 [262,340]	11.8 [10.2,13.2]
Sinaloa	0.81	3156674	455	144.0	233 [200,260]	7.4 [6.3,8.2]
Puebla	0.84	6604451	339	51.3	180 [153,202]	2.7 [2.3,3.1]
Quintana Roo	0.56	1723259	338	196.0	196 [168,220]	11.4 [9.7,12.8]
Chihuahua	0.54	3801487	305	80.2	211 [178,238]	5.5 [4.7,6.2]
Hidalgo	0.90	3086414	266	86.2	255 [215,289]	8.3 [7,9.3]
Morelos	0.87	2044058	262	128.0	107 [89.2,121]	5.2 [4.4,5.9]
Guerrero	1.00	3657048	251	68.6	178 [149,202]	4.9 [4.1,5.5]
Michoacán	0.91	4825401	148	30.7	121 [98.1,140]	2.5 [2,2.9]
Oaxaca	1.10	4143593	138	33.3	131 [106,150]	3.1 [2.5,3.6]
Yucatán	0.90	2259098	138	61.1	92.9 [74.5,108]	4.1 [3.3,4.8]
Tlaxcala	0.74	1380011	136	98.5	113 [91.1,131]	8.2 [6.6,9.5]
Jalisco	0.57	8409693	132	15.7	223 [179,258]	2.6 [2.1,3.1]
Chiapas	0.82	5730367	125	21.8	258 [200,302]	4.5 [3.5,5.3]
Sonora	0.56	3074745	113	36.8	205 [166,237]	6.7 [5.4,7.7]
Guanajuato	0.73	6228175	105	16.9	95.9 [75.5,112]	1.5 [1.2,1.8]

Our estimated IFRs for each of the states range from 0.36% to 1.1%. In the three states accounting for almost half of the deaths, we estimate that the percentage of people that have been infected with SARS-CoV-2 ranges from 17.1% (95% Confidence Interval (CI): 15%-18.8%) in Mexico City, 6.3% (95% CI: 5.5%-7%) in the Estado de México, and 23.2% (95% CI: 20.4%-25.6%) in Baja California.

The following figures show the estimates of infections, deaths and \(R_t\). For each state the first plot has the daily number of infections, brown bars are reported cases, blue bands are predicted infections, dark blue 50% CI, and light blue 95% CI. The second plot shows daily number of deaths, brown bars are reported deaths, pink bars are estimated deaths yet unreported because of reporting lag, blue bands are predicted deaths, and CI as in the first plot. The third plot is the time-varying reproduction number \(R_t\), dark green 50% CI, light green 95% CI. Icons are interventions shown at the time they occurred.

The reproduction number at the start of the epidemic meant that an infected individual would infect three or four others on average. If the reproduction number is above 1, the number of infections continues to grow. Following non-pharmaceutical interventions such as school closures and decreases in population mobility, our results show substantial reductions in the estimated value of \(R_t\) in each state. However, the reproduction number remains mainly above 1, meaning that the epidemic is not yet controlled and will continue to grow. As an example, we can compare the plots of Mexico City, Baja California and Quintana Roo. Mexico City has a reproduction number slightly above 1, which translates to a linear growth of its cases, Baja California seems to have a constant \(R_t\) at 1, which is reflected in a constant rate of daily cases. Quintana Roo managed to reduce its \(R_t\) to less than 1, so cases have decreased and the epidemic seems to be under control.

5 Discussion

The results presented here suggest an ongoing epidemic in which substantial reductions in the average reproduction number have been achieved through non-pharmaceutical interventions. However, our results also show that so far the changes in mobility have not been enough to reduce the reproduction number below 1. Therefore we predict continued growth of the epidemic across Mexico and increases in the associated number of cases and deaths unless further actions are taken.

Our results also reveal extensive heterogeneity in predicted attack rates between states, suggesting that the epidemic is at a far more advanced stage in some states compared to others. Despite this, a small proportion of individuals within each state has been infected to date, indicating that herd immunity is not close yet.

There is still a lot to be done regarding the adjustment in death-delayed reporting. We are trying different models to improve the fit and reflect the uncertainty. Also, we will be able to set a prior distribution to death underreporting for each state when more data is available. The state-level infection fatality ratio can also be improved, for example, we could use other data such as comorbidities or the number of hospital beds available to calculate the IFR of each state. Furthermore, seroprevalence studies would give much more precise information on the rate.

To conclude, let us highlight that this model uses mobility to predict the rate of transmission, neglecting the potential effect of additional behavioural changes or interventions such as increased mask wearing, changes in age specific movement, testing and tracing. Therefore, the scenarios are pessimistic in nature and should be interpreted as such.

6 Acknowledgements

We thank Paulina Preciado from geek end for her support during the elaboration of this work.

References

[1] Seth Flaxman et al. “Report 13: Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries”. In: (2020). https://doi.org/10.25561/77731.

[2] Thomas A Mellan, Henrique H Hoeltgebaum, Swapnil Mishra et al. Estimating COVID-19 cases and reproduction number in Brazil. Imperial College London (08-05-2020), doi: https://doi.org/10.25561/78872.

[3] https://www.worldometers.info/coronavirus/

[4] This phenomenon is explained by Jorge Andrés Castañeda and Sebastián Garrido in ¿Cómo entender los datos de defunciones por COVID-19 en México?

[5] This is published by Mexicanos Contra la Corrupción y la Impunidad in Las actas sobre el número real de muertos con COVID-19 en CDMX

[6] This estimation procedure is explained by Mario Romero Zavala and Laurianne Despeghel in ¿Qué nos dicen las actas de defunción de la CDMX?