Relevant mathematical modelling efforts for understanding COVID-19 dynamics: an educational challenge.

The purpose of the work described in this paper is to emphasize the importance of using mathematical models and mathematical modelling in order to be able to understand and to learn possible behaviours in epidemic situations such as that of the COVID-19 pandemic, besides suggesting modelling techniques with which to evaluate certain sanitary decisions and policies which do, in fact, affect society as a whole. The mathematical tools that are used derive from nonlinear systems of difference equations (possibly viable at a high school level, using spreadsheets or adequate software) as well as nonlinear systems of ordinary differential equations (therefore using mathematical tools and software well within the reach of undergraduate students of many courses). This purpose is accomplished by motivating students and learners to study existing SIR-type models and modifying them in order to have a fully understandable translation of dynamics for infectious diseases such as COVID-19 in several different realistic scenarios, that is to say, situations that consider social distancing policies, widespread vaccination programmes, as well as possible and even probable results when in the presence of negationist postures and attitudes. Several modelling choices referring to real-life situations are shown and explored. These models are analysed and discussed, implicitly proposing similar attitudes and evaluations in learning environments. Conclusions are drawn, stimulating further work using the described mathematical tools and resources. Supplementary Information: The online version contains supplementary material available at 10.1007/s11858-022-01447-2.

Modeling and Global Sensitivity Analysis of Strategies to Mitigate Covid-19 Transmission on a Structured College Campus.

In response to the COVID-19 pandemic, many higher educational institutions moved their courses on-line in hopes of slowing disease spread. The advent of multiple highly-effective vaccines offers the promise of a return to "normal" in-person operations, but it is not clear if-or for how long-campuses should employ non-pharmaceutical interventions such as requiring masks or capping the size of in-person courses. In this study, we develop and fine-tune a model of COVID-19 spread to UC Merced's student and faculty population. We perform a global sensitivity analysis to consider how both pharmaceutical and non-pharmaceutical interventions impact disease spread. Our work reveals that vaccines alone may not be sufficient to eradicate disease dynamics and that significant contact with an infectious surrounding community will maintain infections on-campus. Our work provides a foundation for higher-education planning allowing campuses to balance the benefits of in-person instruction with the ability to quarantine/isolate infectious individuals.

Decoding the double trouble: A mathematical modelling of co-infection dynamics of SARS-CoV-2 and influenza-like illness.

After the detection of coronavirus disease 2019 (Covid-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Wuhan, Hubei Province, China in late December, the cases of Covid-19 have spiralled out around the globe. Due to the clinical similarity of Covid-19 with other flulike syndromes, patients are assayed for other pathogens of influenza like illness. There have been reported cases of co-infection amongst patients with Covid-19. Bacteria for example Streptococcus pneumoniae, Staphylococcus aureus, Klebsiella pneumoniae, Mycoplasma pneumoniae, Chlamydia pneumonia, Legionella pneumophila etc and viruses such as influenza, coronavirus, rhinovirus/enterovirus, parainfluenza, metapneumovirus, influenza B virus etc are identified as co-pathogens. In our current effort, we develop and analysed a compartmental based Ordinary Differential Equation (ODE) type mathematical model to understand the co-infection dynamics of Covid-19 and other influenza type illness. In this work we have incorporated the saturated treatment rate to take account of the impact of limited treatment resources to control the possible Covid-19 cases. As results, we formulate the basic reproduction number of the model system. Finally, we have performed numerical simulations of the co-infection model to examine the solutions in different zones of parameter space.

Analysis of the Adomian decomposition method to estimate the COVID-19 pandemic

Several techniques, including mathematical models, have been explored since the onset of COVID-19 transmission to evaluate the end outcome and implement drastic measures for this illness. Using the currently infected, noninfected, exposed, susceptible, and recovered cases in the Indian community, we created a mathematical model to describe the transmission of COVID-19. In particular, we used the semianalytical Adomian decomposition method without considering any discretization to perform the first-order differential equations related to COVID-19 cases. According to our early findings, rigorous initial isolation for 22-25days would reduce the number of exposed and newly infected people. As a result of the downstream effect, the number of suspected and recovered persons would remain stable, assuming that social distance is properly recognized. In a larger sense, the parameters established by our mathematical model may aid in the refinement of future pandemic tactics. © 2022 Elsevier Inc. All rights reserved.

Mathematical Model for Medium-Term Covid-19 Forecasts in Kazakhstan

In this paper has been formulated and solved the problem of identifying unknown parameters of the mathematical model describing the spread of COVID-19 infection in Kazakhstan, based on additional statistical information about infected, recovered and fatal cases. The considered model, which is part of the family of modified models based on the SIR model developed by W. Kermak and A. McKendrick in 1927, is presented as a system of 5 nonlinear ordinary differential equations describing the variational transition of individuals from one group to another. By solving the inverse problem, reduced to solving the optimization problem of minimizing the functional, using the differential evolution algorithm proposed by Rainer Storn and Kenneth Price in 1995 on the basis of simple evolutionary problems in biology, the model parameters were refined and made a forecast and predicted a peak of infected, recovered and deaths among the population of the country. The differential evolution algorithm includes the generation of populations of probable solutions randomly created in a predetermined space, sampling of the algorithm's stopping criterion, mutation, crossing and selection.

Robustness analysis for quantitative assessment of vaccination effects and SARS-CoV-2 lineages in Italy.

BACKGROUND: In Italy, the beginning of 2021 was characterized by the emergence of new variants of SARS-CoV-2 and by the availability of effective vaccines that contributed to the mitigation of non-pharmaceutical interventions and to the avoidance of hospital collapse. METHODS: We analyzed the COVID-19 propagation in Italy starting from September 2021 with a Susceptible-Exposed-Infected-Recovered (SEIR) model that takes into account SARS-CoV-2 lineages, intervention measures and efficacious vaccines. The model was calibrated with the Bayesian method Conditional Robust Calibration (CRC) using COVID-19 data from September 2020 to May 2021. Here, we apply the Conditional Robustness Analysis (CRA) algorithm to the calibrated model in order to identify model parameters that most affect the epidemic diffusion in the long-term scenario. We focus our attention on vaccination and intervention parameters, which are the key parameters for long-term solutions for epidemic control. RESULTS: Our model successfully describes the presence of new variants and the impact of vaccinations and non-pharmaceutical interventions in the Italian scenario. The CRA analysis reveals that vaccine efficacy and waning immunity play a crucial role for pandemic control, together with asymptomatic transmission. Moreover, even though the presence of variants may impair vaccine effectiveness, virus transmission can be kept low with a constant vaccination rate and low restriction levels. CONCLUSIONS: In the long term, a policy of booster vaccinations together with contact tracing and testing will be key strategies for the containment of SARS-CoV-2 spread.

Application of Mathematical Modeling in Prediction of COVID-19 Transmission Dynamics.

The entire world has been affected by the outbreak of COVID-19 since early 2020. Human carriers are largely the spreaders of this new disease, and it spreads much faster compared to previously identified coronaviruses and other flu viruses. Although vaccines have been invented and released, it will still be a challenge to overcome this disease. To save lives, it is important to better understand how the virus is transmitted from one host to another and how future areas of infection can be predicted. Recently, the second wave of infection has hit multiple countries, and governments have implemented necessary measures to tackle the spread of the virus. We investigated the three phases of COVID-19 research through a selected list of mathematical modeling articles. To take the necessary measures, it is important to understand the transmission dynamics of the disease, and mathematical modeling has been considered a proven technique in predicting such dynamics. To this end, this paper summarizes all the available mathematical models that have been used in predicting the transmission of COVID-19. A total of nine mathematical models have been thoroughly reviewed and characterized in this work, so as to understand the intrinsic properties of each model in predicting disease transmission dynamics. The application of these nine models in predicting COVID-19 transmission dynamics is presented with a case study, along with detailed comparisons of these models. Toward the end of the paper, key behavioral properties of each model, relevant challenges and future directions are discussed.

A vaccination model for COVID-19 in Gauteng, South Africa.

The COVID-19 pandemic provides an opportunity to explore the impact of government mandates on movement restrictions and non-pharmaceutical interventions on a novel infection, and we investigate these strategies in early-stage outbreak dynamics. The rate of disease spread in South Africa varied over time as individuals changed behavior in response to the ongoing pandemic and to changing government policies. Using a system of ordinary differential equations, we model the outbreak in the province of Gauteng, assuming that several parameters vary over time. Analyzing data from the time period before vaccination gives the approximate dates of parameter changes, and those dates are linked to government policies. Unknown parameters are then estimated from available case data and used to assess the impact of each policy. Looking forward in time, possible scenarios give projections involving the implementation of two different vaccines at varying times. Our results quantify the impact of different government policies and demonstrate how vaccinations can alter infection spread.

A transmission dynamics model of COVID-19: Case of Cameroon.

In this work, we propose and investigate an ordinary differential equations model describing the spread of COVID-19 in Cameroon. The model takes into account the asymptomatic, unreported symptomatic, quarantine, hospitalized individuals and the amount of virus in the environment, for evaluating their impact on the transmission of the disease. After establishing the basic properties of the model, we compute the control reproduction number R c and show that the disease dies out whenever R c ≤ 1 and is endemic whenever R c > 1 . Furthermore, an optimal control problem is derived and investigated theoretically by mainly relying on Pontryagin's maximum principle. We illustrate the theoretical analysis by presenting some graphical results.

An Improved ISEIRD Model for COVID-19 Trend Simulations

This paper presents an improved SEIRD model (ISEIRD)for COVID-19 Trend Predictions by incorporating birth rate, natural death rate and re-positive rate. The proposed method is evaluated on 448 days of data (March 10, 2020May30, 2021).Our study shows that the ISEIRD model outperforms in simulating the covid-19 infections. The Python simulated results are included in the paper to validate the scheme. © 2021 IEEE.

AN EDUCATIONAL APPROACH FOR MATHEMATICAL MODELS OF COVID-19 PROPAGATION: ODE AND NEURAL NETWOKS

A special type of coronavirus responsible for respiratory illness was first discovered in Wuhan, China in December 2019 and shortly is spreading in the world. Even few vaccines have been developed, actually their effects are not completely studies during few years over a large population, and it is possible that this pandemic to be seasonal in the future, in a similar manner like the flu. An educational tool will be useful for students and research to learn the model of spreading the disease, especially for biomedical engineering students that have knowledge both about the infectious diseases and mathematical modelling. An educational tool for recurrent waves of COVID-19 disease is proposed. The tool uses two general types of models: a compartment one that can be translated in a system of ordinary differential diseases (ODE) and neural network ones. The asymptomatic compartment and quarantine along with possibility of re-infection is taken into account in both models. The lockdown is simulated using few types of continuous function instead on constant transmission rate of disease. A graphic user interface (GUI) is constructed in order to offer to user an intuitive manner to user learn the COVID-19 models. The tool offers the possibility to choose the parameters of models and suggestion for equilibrium stability to the disease-free and endemic equilibrium and calculation of basic reproduction number. A predefined set with collected data for few countries was downloaded from site that maintains the evidence of cases in the world, but also new collected data by user can be loaded into tool to test the models. © 2021, National Defence University - Carol I Printing House. All rights reserved.

A data-driven model for COVID-19 pandemic - Evolution of the attack rate and prognosis for Brazil.

We introduce a compartmental model SEIAHRV (Susceptible, Exposed, Infected, Asymptomatic, Hospitalized, Recovered, Vaccinated) with age structure for the spread of the SARAS-CoV virus. In order to model current different vaccines we use compartments for individuals vaccinated with one and two doses without vaccine failure and a compartment for vaccinated individual with vaccine failure. The model allows to consider any number of different vaccines with different efficacies and delays between doses. Contacts among age groups are modeled by a contact matrix and the contagion matrix is obtained from a probability of contagion pc per contact. The model uses known epidemiological parameters and the time dependent probability pc is obtained by fitting the model output to the series of deaths in each locality, and reflects non-pharmaceutical interventions. As a benchmark the output of the model is compared to two good quality serological surveys, and applied to study the evolution of the COVID-19 pandemic in the main Brazilian cities with a total population of more than one million. We also discuss with some detail the case of the city of Manaus which raised special attention due to a previous report of We also estimate the attack rate, the total proportion of cases (symptomatic and asymptomatic) with respect to the total population, for all Brazilian states since the beginning of the COVID-19 pandemic. We argue that the model present here is relevant to assessing present policies not only in Brazil but also in any place where good serological surveys are not available.

A data-driven model of the COVID-19 spread among interconnected populations: epidemiological and mobility aspects following the lockdown in Italy.

An epidemic multi-group model formed by interconnected SEIR-like structures is formulated and used for data fitting to gain insight into the COVID-19 dynamics and into the role of non-pharmaceutical control actions implemented to limit the infection spread since its outbreak in Italy. The single submodels provide a rather accurate description of the COVID-19 evolution in each subpopulation by an extended SEIR model including the class of asymptomatic infectives, which is recognized as a determinant for disease diffusion. The multi-group structure is specifically designed to investigate the effects of the inter-regional mobility restored at the end of the first strong lockdown in Italy (June 3, 2020). In its time-invariant version, the model is shown to enjoy some analytical stability properties which provide significant insights on the efficacy of the implemented control measurements. In order to highlight the impact of human mobility on the disease evolution in Italy between the first and second wave onset, the model is applied to fit real epidemiological data of three geographical macro-areas in the period March-October 2020, including the mass departure for summer holidays. The simulation results are in good agreement with the data, so that the model can represent a useful tool for predicting the effects of the combination of containment measures in triggering future pandemic scenarios. Particularly, the simulation shows that, although the unrestricted mobility alone appears to be insufficient to trigger the second wave, the human transfers were crucial to make uniform the spatial distribution of the infection throughout the country and, combined with the restart of the production, trade, and education activities, determined a time advance of the contagion increase since September 2020.

Deterministic and stochastic models for the epidemic dynamics of COVID-19 in Wuhan, China.

In this paper, deterministic and stochastic models are proposed to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Wuhan, China. The deterministic model is formulated by a system of ordinary differential equations (ODEs) that is built upon the classical SEIR framework. The stochastic model is formulated by a continuous-time Markov chain (CTMC) that is derived based on the ODE model with constant parameters. The nonlinear CTMC model is approximated by a multitype branching process to obtain an analytical estimate for the probability of a disease outbreak. The local and global dynamics of the disease are analyzed by using the deterministic model with constant parameters, and the result indicates that the basic reproduction number $ \mathcal{R}_0 $ serves as a sharp disease threshold: the disease dies out if $ \mathcal{R}_0\le 1 $ and persists if $ \mathcal{R}_0 > 1 $. In contrast to the deterministic dynamics, the stochastic dynamics indicate that the disease may not persist when $ \mathcal{R}_0 > 1 $. Parameter estimation and validation are performed to fit our ODE model to the public reported data. Our result indicates that both the exposed and infected classes play an important role in shaping the epidemic dynamics of COVID-19 in Wuhan, China. In addition, numerical simulations indicate that a second wave of the ongoing pandemic is likely to occur if the prevention and control strategies are not implemented properly.