Modeling the COVID-19 Pandemic Using an SEIHR Model With Human Migration

Dynamics of a susceptible-infected-recovered model on complex networks with interregional migration

We present a susceptible-infected-recovered model based on a dynamic flow network that describes the epidemic process on complex metapopulation networks. This model views population regions as interconnected nodes and describes the evolution of each region using a system of differential equations. The next-generation matrix method is used to derive the global basic reproduction number for three cases: a general network with homogeneous infection rates in all regions, a fully connected network, and a star network with heterogeneous infection and recovery rates. For the homogeneous case, we show that this global basic reproduction number is independent of the migration rates between regions. However, the rate of convergence of each region to an equilibrium state exhibits a much larger variance in random (Erdős-Rényi) networks compared to small-scale (Barabási-Albert) networks. For the general heterogeneous case, we report interesting results, namely that the global basic reproduction number decays exponentially with respect to the smallest nonzero Laplacian eigenvalue (algebraic connectivity). Furthermore, we demonstrate both analytically and numerically that as the network's algebraic connectivity increases, either by increasing the average node degree of each region or the global migration rate, the global basic reproduction number decreases and converges to the ratio of the average local infection rate to the average local recovery rate, meaning that the lower bound of the global basic reproduction rate does not equal the mean of local basic reproduction rates.

Modeling the Impact of Vaccination on COVID-19 and Its Delta and Omicron Variants

Vaccination is an important means to fight against the spread of the SARS-CoV-2 virus and its variants. In this work, we propose a general susceptible-vaccinated-exposed-infected-hospitalized-removed (SVEIHR) model and derive its basic and effective reproduction numbers. We set Hong Kong as an example and calculate conditions of herd immunity for multiple vaccines and disease variants. The model shows how the number of confirmed COVID-19 cases in Hong Kong during the second and third waves of the COVID-19 pandemic would have been reduced if vaccination were available then. We then investigate the relationships between various model parameters and the cumulative number of hospitalized COVID-19 cases in Hong Kong for the ancestral, Delta, and Omicron strains. Numerical results demonstrate that the static herd immunity threshold corresponds to one percent of the population requiring hospitalization or isolation at some point in time. We also demonstrate that when the vaccination rate is high, the initial proportion of vaccinated individuals can be lowered while still maintaining the same proportion of cumulative hospitalized/isolated individuals.

An Enhanced SEIR Model for Prediction of COVID-19 with Vaccination Effect

Currently, the spread of COVID-19 is running at a constant pace. The current situation is not so alarming, but every pandemic has a history of three waves. Two waves have been seen, and now expecting the third wave. Compartmental models are one of the methods that predict the severity of a pandemic. An enhanced SEIR model is expected to predict the new cases of COVID-19. The proposed model has an additional compartment of vaccination. This proposed model is the SEIRV model that predicts the severity of COVID-19 when the population is vaccinated. The proposed model is simulated with three conditions. The first condition is when social distancing is not incorporated, while the second condition is when social distancing is included. The third one condition is when social distancing is combined when the population is vaccinated. The result shows an epidemic growth rate of about 0.06 per day, and the number of infected people doubles every 10.7 days. Still, with imparting social distancing, the proposed model obtained the value of R0 is 1.3. Vaccination of infants and kids will be considered as future work.

A stochastic SEIHR model for COVID-19 data fluctuations

Although deterministic compartmental models are useful for predicting the general trend of a disease's spread, they are unable to describe the random daily fluctuations in the number of new infections and hospitalizations, which is crucial in determining the necessary healthcare capacity for a specified level of risk. In this paper, we propose a stochastic SEIHR (sSEIHR) model to describe such random fluctuations and provide sufficient conditions for stochastic stability of the disease-free equilibrium, based on the basic reproduction number that we estimated. Our extensive numerical results demonstrate strong threshold behavior near the estimated basic reproduction number, suggesting that the necessary conditions for stochastic stability are close to the sufficient conditions derived. Furthermore, we found that increasing the noise level slightly reduces the final proportion of infected individuals. In addition, we analyze COVID-19 data from various regions worldwide and demonstrate that by changing only a few parameter values, our sSEIHR model can accurately describe both the general trend and the random fluctuations in the number of daily new cases in each region, allowing governments and hospitals to make more accurate caseload predictions using fewer compartments and parameters than other comparable stochastic compartmental models.

A Novel Ensemble-based Classifier for Detecting the COVID-19 Disease for Infected Patients

The recently discovered coronavirus, SARS-CoV-2, which was detected in Wuhan, China, has spread worldwide and is still being studied at the end of 2019. Detection of COVID-19 at an early stage is essential to provide adequate healthcare to affected patients and protect the uninfected community. This paper aims to design and develop a novel ensemble-based classifier to predict COVID-19 cases at a very early stage so that appropriate action can be taken by patients, doctors, health organizations, and the government. In this paper, a synthetic dataset of COVID-19 is generated by a dataset generation algorithm. A novel ensemble-based classifier of machine learning is employed on the COVID-19 dataset to predict the disease. A convex hull-based approach is also applied to the data to improve the proposed novel, ensemble-based classifier's accuracy and speed. The model is designed and developed through the python programming language and compares with the most popular classifier, i.e., Decision Tree, ID3, and support vector machine. The results indicate that the proposed novel classifier provides a more significant precision, kappa static, root means a square error, recall, F-measure, and accuracy.

Mathematical model for COVID-19 management in crowded settlements and high-activity areas

This paper develops and analyses a habitat area size dependent mathematical model to study the transmission dynamics of COVID-19 in crowded settlements such as refugee camps, schools, markets and churches. The model quantifies the potential impact of physical/social distancing and population density on the disease burden. Results reveal that with no fatalities and no infected entrants, the reproduction numbers associated with asymptomatic and symptomatic cases are inversely proportional to; the habitat area size, and the efforts employed in tracing and hospitalising these cases. The critical habitat area below which the disease dies out is directly proportion to the time taken to identify and hospitalise infected individuals. Results also show that disease persistence in the community is guaranteed even with minimal admission of infected individuals. Our results further show that as the level of compliance to standard operating procedures (SOPs) increases, then the disease prevalence peaks are greatly reduced and delayed. Therefore, proper adherence to SOPs such as use of masks, physical distancing measures and effective contact tracing should be highly enforced in crowded settings if COVID-19 is to be mitigated.