Data-driven mathematical modeling approaches for COVID-19: A survey

In this review, we successively present the methods for phenomenological modeling of the evolution of reported and unreported cases of COVID-19, both in the exponential phase of growth and then in a complete epidemic wave. After the case of an isolated wave, we present the modeling of several successive waves separated by endemic stationary periods. Then, we treat the case of multi-compartmental models without or with age structure. Eventually, we review the literature, based on 260 articles selected in 11 sections, ranging from the medical survey of hospital cases to forecasting the dynamics of new cases in the general population. This review favors the phenomenological approach over the mechanistic approach in the choice of references and provides simulations of the evolution of the number of observed cases of COVID-19 for 10 states (California, China, France, India, Israel, Japan, New York, Peru, Spain and United Kingdom).

Association between ambient temperature and influenza prevalence: A nationwide time-series analysis in 201 Chinese cities from 2013 to 2018

BACKGROUND

Temperature affects influenza transmission; however, currently, limited evidence exists about its effect in China at the national and city levels as well as how temperature can be integrated into influenza interventions.

METHODS

Meteorological, pollutant, and influenza data from 201 cities in mainland China between 2013 and 2018 were analyzed at both the city and national levels to investigate the relationship between temperature and influenza prevalence. We examined the impact of temperature on the time-varying reproduction number (Rt) using generalized additive quasi-Poisson regression models combined with the distributed lag nonlinear model. Threshold temperatures were determined for seven regions based on the early warning threshold of serious influenza outbreaks, set at Rt = 1.2. A multivariate random-effects meta-analysis was employed to assess region-specific associations. The excess risk (ER) index was defined to investigate the correlation between Rt and temperature, modified based on seasonal and regional characteristics.

RESULTS

At the national level and in the central, northern, northwestern, and southern regions, temperature was found to be negatively correlated with relative risk, whereas the shapes of the data curves for the eastern, southwestern, and northeastern regions were not well defined. Low temperatures had an observable effect on influenza prevalence; however, the effects of high temperatures were not obvious. At an Rt of 1.2, the threshold temperatures for reaching a warning for serious influenza outbreaks were - 24.3 °C in the northeastern region, 16.6 °C in the northwestern region, and between 1℃ and 10 °C in other regions.

CONCLUSION

The study findings revealed that temperature had a varying effect on influenza transmission trends (Rt) across different regions in China. By identifying region-specific temperature thresholds at Rt = 1.2, more effective early warning systems for influenza outbreaks could be tailored. These findings emphasize the significance of the region-specific adaptation of influenza prevention and control measures.

Maximal reproduction number estimation and identification of transmission rate from the first inflection point of new infectious cases waves: COVID-19 outbreak example

The dynamics of COVID-19 pandemic varies across countries and it is important for​ researchers to study different kind of phenomena observed at different stages of the waves during the epidemic period. Our interest in this paper is not to model what happened during the endemic state but during the epidemic state. We proposed a continuous formulation of a unique maximum reproduction number estimate with an assumption that the epidemic curve is in form of the Gaussian curve and then compare the model with the discrete form and the observed basic reproduction number during the contagiousness period considered. Furthermore, we estimated the transmission rate from identification of the first inflection point of a wave of the curve of daily new infectious cases using the Bernoulli S-I (Susceptible-Infected) equation. We applied this new method to the real data from Cameroon COVID-19 outbreak both at national and regional levels. High correlation was observed between the socio-economic parameters and epidemiology parameters at regional level in Cameroon. Also, the method was applied to the second wave COVID-19 outbreak for the world data which is a period the phenomena we are considering were observed. Lastly, it was observed that the models presented results correspond with the epidemic dynamics in Cameroon and World data. We recommend that it is important to study what happened during the growth inflection point as some countries data did not climax.

Modeling and control of epidemics through testing policies

Testing is a crucial control mechanism in the beginning phase of an epidemic when the vaccines are not yet available. It enables the public health authority to detect and isolate the infected cases from the population, thereby limiting the disease transmission to susceptible people. However, despite the significance of testing in epidemic control, the recent literature on the subject lacks a control-theoretic perspective. In this paper, an epidemic model is proposed that incorporates the testing rate as a control input and differentiates the undetected infected from the detected infected cases, who are assumed to be removed from the disease spreading process in the population. After estimating the model on the data corresponding to the beginning phase of COVID-19 in France, two testing policies are proposed: the so-called best-effort strategy for testing (BEST) and constant optimal strategy for testing (COST). The BEST policy is a suppression strategy that provides a minimum testing rate that stops the growth of the epidemic when implemented. The COST policy, on the other hand, is a mitigation strategy that provides an optimal value of testing rate minimizing the peak value of the infected population when the total stockpile of tests is limited. Both testing policies are evaluated by their impact on the number of active intensive care unit (ICU) cases and the cumulative number of deaths for the COVID-19 case of France.

Parameter Estimation and Prediction of COVID-19 Epidemic Turning Point and Ending Time of a Case Study on SIR/SQAIR Epidemic Models

In this paper, the SIR epidemiological model for the COVID-19 with unknown parameters is considered in the first strategy. Three curves (S, I, and R) are fitted to the real data of South Korea, based on a detailed analysis of the actual data of South Korea, taken from the Korea Disease Control and Prevention Agency (KDCA). Using the least square method and minimizing the error between the fitted curve and the actual data, unknown parameters, like the transmission rate, recovery rate, and mortality rate, are estimated. The goodness of fit model is investigated with two criteria (SSE and RMSE), and the uncertainty range of the estimated parameters is also presented. Also, using the obtained determined model, the possible ending time and the turning point of the COVID-19 outbreak in the United States are predicted. Due to the lack of treatment and vaccine, in the next strategy, a new group called quarantined people is added to the proposed model. Also, a hidden state, including asymptomatic individuals, which is very common in COVID-19, is considered to make the model more realistic and closer to the real world. Then, the SIR model is developed into the SQAIR model. The delay in the recovery of the infected person is also considered as an unknown parameter. Like the previous steps, the possible ending time and the turning point in the United States are predicted. The model obtained in each strategy for South Korea is compared with the actual data from KDCA to prove the accuracy of the estimation of the parameters.

Estimating the real burden of disease under a pandemic situation: The SARS-CoV2 case

The present paper introduces a new model used to study and analyse the severe acute respiratory syndrome coronavirus 2 (SARS-CoV2) epidemic-reported-data from Spain. This is a Hidden Markov Model whose hidden layer is a regeneration process with Poisson immigration, Po-INAR(1), together with a mechanism that allows the estimation of the under-reporting in non-stationary count time series. A novelty of the model is that the expectation of the unobserved process's innovations is a time-dependent function defined in such a way that information about the spread of an epidemic, as modelled through a Susceptible-Infectious-Removed dynamical system, is incorporated into the model. In addition, the parameter controlling the intensity of the under-reporting is also made to vary with time to adjust to possible seasonality or trend in the data. Maximum likelihood methods are used to estimate the parameters of the model.

Mathematical Parameters of the COVID-19 Epidemic in Brazil and Evaluation of the Impact of Different Public Health Measures

A SIRU-type epidemic model is employed for the prediction of the COVID-19 epidemy evolution in Brazil, and analyze the influence of public health measures on simulating the control of this infectious disease. The proposed model allows for a time variable functional form of both the transmission rate and the fraction of asymptomatic infectious individuals that become reported symptomatic individuals, to reflect public health interventions, towards the epidemy control. An exponential analytical behavior for the accumulated reported cases evolution is assumed at the onset of the epidemy, for explicitly estimating initial conditions, while a Bayesian inference approach is adopted for the estimation of parameters by employing the direct problem model with the data from the first phase of the epidemy evolution, represented by the time series for the reported cases of infected individuals. The evolution of the COVID-19 epidemy in China is considered for validation purposes, by taking the first part of the dataset of accumulated reported infectious individuals to estimate the related parameters, and retaining the rest of the evolution data for direct comparison with the predicted results. Then, the available data on reported cases in Brazil from 15 February until 29 March, is used for estimating parameters and then predicting the first phase of the epidemy evolution from these initial conditions. The data for the reported cases in Brazil from 30 March until 23 April are reserved for validation of the model. Then, public health interventions are simulated, aimed at evaluating the effects on the disease spreading, by acting on both the transmission rate and the fraction of the total number of the symptomatic infectious individuals, considering time variable exponential behaviors for these two parameters. This first constructed model provides fairly accurate predictions up to day 65 below 5% relative deviation, when the data starts detaching from the theoretical curve. From the simulated public health intervention measures through five different scenarios, it was observed that a combination of careful control of the social distancing relaxation and improved sanitary habits, together with more intensive testing for isolation of symptomatic cases, is essential to achieve the overall control of the disease and avoid a second more strict social distancing intervention. Finally, the full dataset available by the completion of the present work is employed in redefining the model to yield updated epidemy evolution estimates.

Modeling the Effects of Meteorological Factors and Unreported Cases on Seasonal Influenza Outbreaks in Gansu Province, China

Influenza usually breaks out seasonally in temperate regions, especially in winter, infection rates and mortality rates of influenza increase significantly, which means that dry air and cold temperatures accelerate the spread of influenza viruses. However, the meteorological factors that lead to seasonal influenza outbreaks and how these meteorological factors play a decisive role in influenza transmission remain unclear. During the epidemic of infectious diseases, the neglect of unreported cases leads to an underestimation of infection rates and basic reproduction number. In this paper, we propose a new non-autonomous periodic differential equation model with meteorological factors including unreported cases. First, the basic reproduction number is obtained and the global asymptotic stability of the disease-free periodic solution is proved. Furthermore, the existence of periodic solutions and the uniformly persistence of the model are demonstrated. Second, the best-fit parameter values in our model are identified by the MCMC algorithm on the basis of the influenza data in Gansu province, China. We also estimate that the basic reproduction number is 1.2288 (95% CI:(1.2287, 1.2289)). Then, to determine the key parameters of the model, uncertainty and sensitivity analysis are explored. Finally, our results show that influenza is more likely to spread in low temperature, low humidity and low precipitation environments. Temperature is a more important factor than relative humidity and precipitation during the influenza epidemic. In addition, our results also show that there are far more unreported cases than reported cases.

Understanding Unreported Cases in the COVID-19 Epidemic Outbreak in Wuhan, China, and the Importance of Major Public Health Interventions

We develop a mathematical model to provide epidemic predictions for the COVID-19 epidemic in Wuhan, China. We use reported case data up to 31 January 2020 from the Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commission to parameterize the model. From the parameterized model, we identify the number of unreported cases. We then use the model to project the epidemic forward with varying levels of public health interventions. The model predictions emphasize the importance of major public health interventions in controlling COVID-19 epidemics.