Early stage COVID-19 disease dynamics in Germany: models and parameter identification

A hybrid compartmental model with a case study of COVID-19 in Great Britain and Israel

Given the severe impact of COVID-19 on several societal levels, it is of crucial importance to model the impact of restriction measures on the pandemic evolution, so that governments are able to make informed decisions. Even though there have been countless attempts to propose diverse models since the rise of the outbreak, the increase in data availability and start of vaccination campaigns calls for updated models and studies. Furthermore, most of the works are focused on a very particular place or application and we strive to attain a more general model, resorting to data from different countries. In particular, we compare Great Britain and Israel, two highly different scenarios in terms of vaccination plans and social structure. We build a network-based model, complex enough to model different scenarios of government-mandated restrictions, but generic enough to be applied to any population. To ease the computational load we propose a decomposition strategy for our model.

A Mathematical Evaluation of the Cost-Effectiveness of Self-Protection, Vaccination, and Disinfectant Spraying for COVID-19 Control

The world is on its path from the post-COVID period, but a fresh wave of the coronavirus infection engulfing most European countries makes the pandemic catastrophic. Mathematical models are of significant importance in unveiling strategies that could stem the spread of the disease. In this paper, a deterministic mathematical model of COVID-19 is studied to characterize a range of feasible control strategies to mitigate the disease. We carried out an analytical investigation of the model’s dynamic behaviour at its equilibria and observed that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number, ${\mathcal{R}}_0$ is less than unity. The endemic equilibrium is also shown to be globally asymptotically stable when ${\mathcal{R}}_0>1$ . Further, we showed that the model exhibits forward bifurcation around ${\mathcal{R}}_0=1$ . Sensitivity analysis was carried out to determine the impact of various factors on the basic reproduction number ${\mathcal{R}}_0$ and consequently, the spread of the disease. An optimal control problem was formulated from the sensitivity analysis. Cost-effectiveness analysis is conducted to determine the most cost-effective strategy that can be adopted to control the spread of COVID-19. The investigation revealed that combining self-protection and environmental control is the most cost-effective control strategy among the enlisted strategies.

Modeling approaches for early warning and monitoring of pandemic situations as well as decision support

The COVID-19 pandemic has highlighted the lack of preparedness of many healthcare systems against pandemic situations. In response, many population-level computational modeling approaches have been proposed for predicting outbreaks, spatiotemporally forecasting disease spread, and assessing as well as predicting the effectiveness of (non-) pharmaceutical interventions. However, in several countries, these modeling efforts have only limited impact on governmental decision-making so far. In light of this situation, the review aims to provide a critical review of existing modeling approaches and to discuss the potential for future developments.

Mathematical modelling of earlier stages of COVID-19 transmission dynamics in Ghana

In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in Wuhan, China and later spread to every corner of the globe. Whilst the number of infection-induced deaths in Ghana, West Africa are minimal when compared with the rest of the world, the impact on the local health service is still significant. Compartmental models are a useful framework for investigating transmission of diseases in societies. To understand how the infection will spread and how to limit the outbreak. We have developed a modified SEIR compartmental model with nine compartments (CoVCom9) to describe the dynamics of SARS-CoV-2 transmission in Ghana. We have carried out a detailed mathematical analysis of the CoVCom9, including the derivation of the basic reproduction number, R 0 . In particular, we have shown that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 via a candidate Lyapunov function. Using the SARS-CoV-2 reported data for confirmed-positive cases and deaths from March 13 to August 10, 2020, we have parametrised the CoVCom9 model. The results of this fit show good agreement with data. We used Latin hypercube sampling-rank correlation coefficient (LHS-PRCC) to investigate the uncertainty and sensitivity of R 0 since the results derived are significant in controlling the spread of SARS-CoV-2. We estimate that over this five month period, the basic reproduction number is given by R 0 = 3 . 110 , with the 95% confidence interval being 2 . 042 ≤ R 0 ≤ 3 . 240 , and the mean value being R 0 = 2 . 623 . Of the 32 parameters in the model, we find that just six have a significant influence on R 0 , these include the rate of testing, where an increasing testing rate contributes to the reduction of R 0 .

Transmission dynamics model and the coronavirus disease 2019 epidemic: applications and challenges

Since late 2019, the beginning of coronavirus disease 2019 (COVID-19) pandemic, transmission dynamics models have achieved great development and were widely used in predicting and policy making. Here, we provided an introduction to the history of disease transmission, summarized transmission dynamics models into three main types: compartment extension, parameter extension and population-stratified extension models, highlight the key contribution of transmission dynamics models in COVID-19 pandemic: estimating epidemiological parameters, predicting the future trend, evaluating the effectiveness of control measures and exploring different possibilities/scenarios. Finally, we pointed out the limitations and challenges lie ahead of transmission dynamics models.

Fractional dynamical probes in COVID-19 model with control interventions: a comparative assessment of eight most affected countries

The ultimate aim of the article is to predict COVID-19 virus inter-cellular behavioral dynamics using an infection model with a quarantine compartment. Internal viral dynamics and stability attributes are thoroughly investigated around stable equilibrium states to probe possible ways in reducing rapid spread by incorporating fractional-order components into epidemic systems. Furthermore, a fractional optimal problem was built and studied with three control measures to restrict the widespread of COVID-19 infections and exhibit perfect protection. It is found that by following 60 % of control strategies can eradicate the infectives. Furthermore, the time frame of sixteen months has been divided into four short periods to grasp the pandemic, as the pandemic's parameters change over time. Finally, using real data, we estimated the parameters of the model system and the expression of the basic reproduction number R 0 for the most affected countries, China, USA, UK, Italy, France, Germany, Spain, and Iran.

Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon

This work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). A multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism is proposed first. Indeed, there are human to human virus transmission, human to environment virus transmission, environment to human virus transmission and self-infection by susceptible individuals. The global stability of the disease-free equilibrium is shown when a given threshold T 0 is less or equal to 1 and the basic reproduction number R 0 is calculated. A convergence index T 1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of infectious extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. Using Partial Rank Correlation Coefficient with a three levels fractional experimental design, the sensitivity of  R 0 , T 0 and T 1 to control parameters is evaluated. Following this study, the most significant parameter is the probability of wearing mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into account economic impacts of SARS-CoV-2, optimal fighting strategies are determined and discussed. The study is applied to real and available data from Cameroon with a model fitting. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy against SARS-CoV-2.

Simulation and prediction of dengue outbreaks based on an SIR model with a time-dependent transmission rate including meteorological data. An example for Colombo and Jakarta

Vector-borne diseases can usually be examined with a vector–host model like the [Formula: see text] model. This, however, depends on parameters that contain detailed information about the mosquito population that we usually do not know. For this reason, in this article, we reduce the [Formula: see text] model to an [Formula: see text] model with a time-dependent and periodic transmission rate [Formula: see text]. Since the living conditions of the mosquitos depend on the local weather conditions, meteorological data sets flow into the model in order to achieve a more realistic behavior. The developed [Formula: see text] model is adapted to existing data sets of hospitalized dengue cases in Jakarta (Indonesia) and Colombo (Sri Lanka) using numerical optimization based on Pontryagin’s maximum principle. A previous data analysis shows that the results of this parameter fit are within a realistic range and thus allow further investigations. Based on this, various simulations are carried out and the prediction quality of the model is examined.