Two complementary model-based methods for calculating the risk of international spreading of a novel virus from the outbreak epicentre. The case of COVID-19

Ground reality versus model-based computation of basic reproductive numbers in epidemics

Computation of basic reproductive numbers is one of the primary goals of epidemic modelers. There are several challenges in such computations, especially when the data from the virus transmission networks are not so easy to collect; this makes model validation almost impossible. We provide a technical comment on the precautions to be taken while computing model-based basic reproductive numbers so that the ground realities of such computation are maintained. Basic reproductive numbers need to be adjusted retrospectively to compensate for reporting errors within the epidemic spread networks. Such an adjustment would lead to revised pandemic preparedness and mitigation plans.

Mathematical modelling of the epidemiology of COVID-19 infection in Ghana

In this paper, Covid-19 patients with self-immunity is incorporated in the Susceptible-Exposed-Infected-Quarantined-Recovered ( S E I Q R ) model is applied to describe the epidemiology of Covid-19 infection in Ghana. Based on data on the epidemiology of the Covid-19 infection in Ghana, we observed that, on an average, three persons contract the Covid-19 infection from an infected person daily based using the basic reproductive number ( R o ) derived from the SEIQR model. In addition, the threshold condition for the long term stability of the Covid-19 infection in Ghana is derived from this model. Based on the Dulac criterion, it was observed that for a long period of time the epidemiology of Covid-19 in Ghana will be under control. Again, we observed that both the transmission rate natural death rate of a person in the various classes mostly influence the spread of Covid-19 infection followed by the exposed rate from exposure class to the infected class, then the rate at which an infected person is quarantined and finally, the rate at an exposed person is quarantined. On the other hand, the rate at which an exposed person recovers from his/her have least influence on the spread of Covid-19 infection in the country. Nevertheless, the rates of birth, transmission of Covid-19 infection to a susceptible person, exposure to Covid-19 infection and Covid-19 patient who is quarantined by the facilities provided by the Ghana Health Service ( G H S ) are in direct relationship with R o . However, the rates at which a quarantiner dies from a Covid-19 infection, an infected person dies from a Covid-19 infection, natural death from each class and the recoveries from an infected class, exposed class and quarantined class are in relationship with R o .

Modelling the impact of delaying vaccination against SARS-CoV-2 assuming unlimited vaccine supply

Background

At the moment we have more than 177 million cases and 3.8 million deaths (as of June 2021) around the world and vaccination represents the only hope to control the pandemic. Imperfections in planning vaccine acquisition and difficulties in implementing distribution among the population, however, have hampered the control of the virus so far.

Methods

We propose a new mathematical model to estimate the impact of vaccination delay against the 2019 coronavirus disease (COVID-19) on the number of cases and deaths due to the disease in Brazil. We apply the model to Brazil as a whole and to the State of Sao Paulo, the most affected by COVID-19 in Brazil. We simulated the model for the populations of the State of Sao Paulo and Brazil as a whole, varying the scenarios related to vaccine efficacy and compliance from the populations.

Results

The model projects that, in the absence of vaccination, almost 170 thousand deaths and more than 350 thousand deaths will occur by the end of 2021 for Sao Paulo and Brazil, respectively. If in contrast, Sao Paulo and Brazil had enough vaccine supply and so started a vaccination campaign in January with the maximum vaccination rate, compliance and efficacy, they could have averted more than 112 thousand deaths and 127 thousand deaths, respectively. In addition, for each month of delay the number of deaths increases monotonically in a logarithmic fashion, for both the State of Sao Paulo and Brazil as a whole.

Conclusions

Our model shows that the current delay in the vaccination schedules that is observed in many countries has serious consequences in terms of mortality by the disease and should serve as an alert to health authorities to speed the process up such that the highest number of people to be immunized is reached in the shortest period of time.

Use of the Hayami diffusive wave equation to model the relationship infected-recoveries-deaths of Covid-19 pandemic

Susceptible S-Infected I-Recovered R-Death D (SIRD) compartmental models are often used for modelling of infectious diseases. On the basis of the analogy between SIRD and compartmental models in hydrology, this study makes mathematical formulations developed in hydrology available for modelling in epidemiology. We adapt the Hayami model solution of the diffusive wave equation generally used in hydrological modelling to compartmental I-R-D models in epidemiology by simulating the relationships between the number of infectious I(t), the number of recoveries R(t) and the number of deaths D(t). The Hayami model is easy-to-use, robust and parsimonious. We compare the empirical one-parameter exponential model usually used in SIRD models to the two-parameter Hayami model. Applications were implemented on the recent Covid-19 pandemic. The application on data from 24 countries shows that both models give comparable performances for modelling the I-D relationship. However, for modelling the I-R relationship and the active cases, the exponential model gives fair performances whereas the Hayami model substantially improves the model performances. The Hayami model also presents the advantage that its parameters can be easily estimated from the analysis of the data distributions of I(t), R(t) and D(t). The Hayami model is parsimonious with only two parameters which are useful to compare the temporal evolution of recoveries and deaths in different countries based on different contamination rates and recoveries strategies. This study highlights the interest of knowledge transfer between different scientific disciplines in order to model different processes.

Estimating the effects of reopening of schools on the course of the epidemic of COVID-19

In this paper, we present a method to estimate the risk of reopening of schools illustrated with the case of the State of São Paulo, Brazil. The model showed that, although no death of children would result from the reopening of the schools in the three cities analysed, the risk of asymptomatic and symptomatic cases and secondary cases among teachers, school staff and relatives of the children is not negligible. Although the epidemic hit different regions with different intensities, our model shows that, for regions where the incidence profile is similar to the cities analysed, the risk of reopening of schools is still too high. This in spite of the fact that incidences in these cities were declining in the period of the time considered. Therefore, although we cannot extend the result to the entire country, the overall conclusion is valid for regions with a declining incidence and it is even more valid for regions where incidence is increasing. We assumed a very conservative level of infection transmissibility of children of just 10% as that of adults. In spite of the very low level of transmissibility is assumed, the number of secondary cases caused by infected children among teachers, school staff and relatives varied from 2 to 85. It is, therefore, too soon to have any degree of confidence that reopening of schools before the advent of a vaccine is the right decision to take. The purpose of our model and simulations is to provide a method to estimate the risk of school reopening, although we are sure it could be applied as a guide to public health strategies.

Estimating the effects of reopening of schools on the course of the epidemic of COVID-19

In this paper, we present a method to estimate the risk of reopening of schools illustrated with the case of the State of São Paulo, Brazil. The model showed that, although no death of children would result from the reopening of the schools in the three cities analysed, the risk of asymptomatic and symptomatic cases and secondary cases among teachers, school staff and relatives of the children is not negligible. Although the epidemic hit different regions with different intensities, our model shows that, for regions where the incidence profile is similar to the cities analysed, the risk of reopening of schools is still too high. This in spite of the fact that incidences in these cities were declining in the period of the time considered. Therefore, although we cannot extend the result to the entire country, the overall conclusion is valid for regions with a declining incidence and it is even more valid for regions where incidence is increasing. We assumed a very conservative level of infection transmissibility of children of just 10% as that of adults. In spite of the very low level of transmissibility is assumed, the number of secondary cases caused by infected children among teachers, school staff and relatives varied from 2 to 85. It is, therefore, too soon to have any degree of confidence that reopening of schools before the advent of a vaccine is the right decision to take. The purpose of our model and simulations is to provide a method to estimate the risk of school reopening, although we are sure it could be applied as a guide to public health strategies.

Modelling the impact of contact tracing of symptomatic individuals on the COVID-19 epidemic

OBJECTIVES

With the declining numbers of coronavirus disease 2019 (COVID-19) cases in the state of São Paulo, Brazil, social distancing measures have gradually been lifted. However, the risk of a surge in the number of cases cannot be overlooked. Even with the adoption of nonpharmaceutical interventions, such as restrictions on mass gatherings, wearing of masks, and complete or partial closure of schools, other public health measures may help control the epidemic. We aimed to evaluate the impact of the contact tracing of symptomatic individuals on the COVID-19 epidemic regardless of the use of diagnostic testing.

METHODS

We developed a mathematical model that includes isolation of symptomatic individuals and tracing of contacts to assess the effects of the contact tracing of symptomatic individuals on the COVID-19 epidemic in the state of São Paulo.

RESULTS

For a selection efficacy (proportion of isolated contacts who are infected) of 80%, cases and deaths may be reduced by 80% after 60 days when 5000 symptomatic individuals are isolated per day, each of them together with 10 contacts. On the other hand, for a selection efficacy of 20%, the number of cases and deaths may be reduced by approximately 40% and 50%, respectively, compared with the scenario in which no contact-tracing strategy is implemented.

CONCLUSION

Contact tracing of symptomatic individuals may potentially be an alternative strategy when the number of diagnostic tests available is not sufficient for massive testing.

Quarantine and the risk of COVID-19 importation

Using a stochastic model, we assess the risk of importation-induced local transmission chains in locations seeing few or no local transmissions and evaluate the role of quarantine in the mitigation of this risk. We find that the rate of importations plays a critical role in determining the risk that case importations lead to local transmission chains, more so than local transmission characteristics, i.e. strength of social distancing measures (NPI). The latter influences the severity of the outbreaks when they do take place. Quarantine after arrival in a location is an efficacious way to reduce the rate of importations. Locations that see no or low-level local transmission should ensure that the rate of importations remains low. A high level of compliance with post-arrival quarantine followed by testing achieves this objective with less of an impact than travel restrictions or bans.

Modelling the test, trace and quarantine strategy to control the COVID-19 epidemic in the state of São Paulo, Brazil

Testing for detecting the infection by SARS-CoV-2 is the bridge between the lockdown and the opening of society. In this paper we modelled and simulated a test-trace-and-quarantine strategy to control the COVID-19 outbreak in the State of São Paulo, Brasil. The State of São Paulo failed to adopt an effective social distancing strategy, reaching at most 59% in late March and started to relax the measures in late June, dropping to 41% in 08 August. Therefore, São Paulo relies heavily on a massive testing strategy in the attempt to control the epidemic.

Two alternative strategies combined with economic evaluations were simulated. One strategy included indiscriminately testing the entire population of the State, reaching more than 40 million people at a maximum cost of 2.25 billion USD, that would reduce the total number of cases by the end of 2020 by 90%. The second strategy investigated testing only symptomatic cases and their immediate contacts – this strategy reached a maximum cost of 150 million USD but also reduced the number of cases by 90%.

The conclusion is that if the State of São Paulo had decided to adopt the simulated strategy on April the 1st, it would have been possible to reduce the total number of cases by 90% at a cost of 2.25 billion US dollars for the indiscriminate strategy but at a much smaller cost of 125 million US dollars for the selective testing of symptomatic cases and their contacts.