Modelling COVID-19 epidemic with confirmed cases-driven contact tracing quarantine.

The pandemic of novel coronavirus disease 2019 (COVID-19) has been a severe threat to public health. The policy of close contract tracing quarantine is an effective strategy in controlling the COVID-19 epidemic outbreak. In this paper, we developed a mathematical model of the COVID-19 epidemic with confirmed case-driven contact tracing quarantine, and applied the model to evaluate the effectiveness of the policy of contact tracing and quarantine. The model is established based on the combination of the compartmental model and individual-based model simulations, which results in a closed-form delay differential equation model. The proposed model includes a novel form of quarantine functions to represent the number of quarantine individuals following the confirmed cases every day and provides analytic expressions to study the effects of changing the quarantine rate. The proposed model can be applied to epidemic dynamics during the period of community spread and when the policy of confirmed cases-driven contact tracing quarantine is efficient. We applied the model to study the effectiveness of contact tracing and quarantine. The proposed delay differential equation model can describe the average epidemic dynamics of the stochastic-individual-based model, however, it is not enough to describe the diverse response due to the stochastic effect. Based on model simulations, we found that the policy of contact tracing and quarantine can obviously reduce the epidemic size, however, may not be enough to achieve zero-infectious in a short time, a combination of close contact quarantine and social contact restriction is required to achieve zero-infectious. Moreover, the effect of reducing epidemic size is insensitive to the period of quarantine, there are no significant changes in the epidemic dynamics when the quarantine days vary from 7 to 21 days.

Global stability of a general HTLV-I infection model with Cytotoxic T-Lymphocyte immune response and mitotic transmission

Mathematical models have been considered as a robust tool to support biological and medical studies of human viral infections. The global stability of viral infection models remains an important and largely open research problem. Such results are necessary to evaluate treatment strategies for infections and to establish thresholds for treatment rates. Human T-lymphotropic virus class I (HTLV-I) is a retrovirus which infects the CD4+T cells and causes chronic and deadly diseases. In this article, we developed a general nonlinear system of ODEs which describes the within-host dynamics of HTLV-I under the effect Cytotoxic T-Lymphocytes (CTLs) immunity. The mitotic division of actively infected cells are modeled. We consider general nonlinear functions for the generation, proliferation and clearance rates for all types of cells. The incidence rate of infec-tion is also modeled by a general nonlinear function. These general functions are assumed to satisfy a set of suitable conditions and include several forms presented in the literature. We determine a bounded domain for the system's solutions. We prove the existence of the system's equilibrium points and determine two threshold numbers, the basic reproductive number R0 and the CTL immunity stimulation number R1. We establish the global stability of all equilibrium points by con-structing Lyapunov function and applying Lyapunov-LaSalle asymptotic stability theorem. Under certain conditions it is shown that if R0 <= 1, then the infection-free equilibrium point is globally asymptotically stable (GAS) and the HTLV-I infection is cleared. If R1 < 1 < R0, then the infected equilibrium point without CTL immunity is GAS and the HTLV-I infection becomes chronic with no sustained CTL immune response. If R1 > 1, then the infected equilibrium point with CTL immu-nity is GAS and the infection becomes chronic with persistent CTL immune response. We present numerical simulations for the system by choosing special shapes of the general functions. The effect of Crowley-Martin functional response and mitotic division of actively infected cells on the HTLV-I progression are studied. Our results cover and improve several ones presented in the literature.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).

Heterogeneity is a key factor describing the initial outbreak of COVID-19.

Assessing the transmission potential of emerging infectious diseases, such as COVID-19, is crucial for implementing prompt and effective intervention policies. The basic reproduction number is widely used to measure the severity of the early stages of disease outbreaks. The basic reproduction number of standard ordinary differential equation models is computed for homogeneous contact patterns; however, realistic contact patterns are far from homogeneous, specifically during the early stages of disease transmission. Heterogeneity of contact patterns can lead to superspreading events that show a significantly high level of heterogeneity in generating secondary infections. This is primarily due to the large variance in the contact patterns of complex human behaviours. Hence, in this work, we investigate the impacts of heterogeneity in contact patterns on the basic reproduction number by developing two distinct model frameworks: 1) an SEIR-Erlang ordinary differential equation model and 2) an SEIR stochastic agent-based model. Furthermore, we estimated the transmission probability of both models in the context of COVID-19 in South Korea. Our results highlighted the importance of heterogeneity in contact patterns and indicated that there should be more information than one quantity (the basic reproduction number as the mean quantity), such as a degree-specific basic reproduction number in the distributional sense when the contact pattern is highly heterogeneous.

The within-host viral kinetics of SARS-CoV-2.

In this work, we use a within-host viral dynamic model to describe the SARS-CoV-2 kinetics in the host. Chest radiograph score data are used to estimate the parameters of that model. Our result shows that the basic reproductive number of SARS-CoV-2 in host growth is around 3.79. Using the same method we also estimate the basic reproductive number of MERS virus is 8.16 which is higher than SARS-CoV-2. The PRCC method is used to analyze the sensitivities of model parameters. Moreover, the drug effects on virus growth and immunity effect of patients are also implemented to analyze the model.

Influence of isolation measures for patients with mild symptoms on the spread of COVID-19.

During the transmission of COVID-19, the hospital isolation of patients with mild symptoms has been a concern. In this paper, we use a differential equation model to describe the propagation of COVID-19, and discuss the effects of intensity of hospital isolation and moment of taking measures on development of the epidemic. The results show that isolation measures can significantly reduce the epidemic final size and the number of dead, and the greater the intensity of measures, the better, but duration of the epidemic will be prolonged. Whenever isolation measures are taken, the epidemic final size and the number of dead can be reduced. In early stage of the epidemic, taking measures one day later has little impact, but after a certain period, if taking measures one day later, the epidemic final size and the number of dead increase sharply. Taking measures as early as possible makes the maximum number of patients appear later, which is conducive to expanding medical bed resources and reducing the pressure on medical resource demand. As long as possible, high-intensity isolation measures should be taken in time for patients with mild symptoms.