Continuous-time stochastic processes for the spread of COVID-19 disease simulated via a Monte Carlo approach and comparison with deterministic models

A mathematical model to assess the impact of testing and isolation compliance on the transmission of COVID-19

The COVID-19 pandemic has ravaged global health and national economies worldwide. Testing and isolation are effective control strategies to mitigate the transmission of COVID-19, especially in the early stage of the disease outbreak. In this paper, we develop a deterministic model to investigate the impact of testing and compliance with isolation on the transmission of COVID-19. We derive the control reproduction number R C , which gives the threshold for disease elimination or prevalence. Using data from New York State in the early stage of the disease outbreak, we estimate R C = 7.989 . Both elasticity and sensitivity analyses show that testing and compliance with isolation are significant in reducing R C and disease prevalence. Simulation reveals that only high testing volume combined with a large proportion of individuals complying with isolation have great impact on mitigating the transmission. The testing starting date is also crucial: the earlier testing is implemented, the more impact it has on reducing the infection. The results obtained here would also be helpful in developing guidelines of early control strategies for pandemics similar to COVID-19.

The Role of Mobility in the Dynamics of the COVID-19 Epidemic in Andalusia

Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively used in the context of the ongoing COVID-19 pandemic. In the present work, we revisit such a model, bearing a particular case example in mind, namely that of the region of Andalusia in Spain during the period of the summer-fall of 2020 (i.e., between the first and second pandemic waves). Our aim is to consider the possibility of incorporation of mobility across the province nodes focusing on mobile-phone time-dependent data, but also discussing the comparison for our case example with a gravity model, as well as with the dynamics in the absence of mobility. Our main finding is that mobility is key toward a quantitative understanding of the emergence of the second wave of the pandemic and that the most accurate way to capture it involves dynamic (rather than static) inclusion of time-dependent mobility matrices based on cell-phone data. Alternatives bearing no mobility are unable to capture the trends revealed by the data in the context of the metapopulation model considered herein.

Stochastic analysis of a COVID-19 model with effects of vaccination and different transition rates: Real data approach

This paper presents a stochastic model for COVID-19 that takes into account factors such as incubation times, vaccine effectiveness, and quarantine periods in the spread of the virus in symptomatically contagious populations. The paper outlines the conditions necessary for the existence and uniqueness of a global solution for the stochastic model. Additionally, the paper employs nonlinear analysis to demonstrate some results on the ergodic aspect of the stochastic model. The model is also simulated and compared to deterministic dynamics. To validate and demonstrate the usefulness of the proposed system, the paper compares the results of the infected class with actual cases from Iraq, Bangladesh, and Croatia. Furthermore, the paper visualizes the impact of vaccination rates and transition rates on the dynamics of infected people in the infected class.

A multi-strain model with asymptomatic transmission: Application to COVID-19 in the US

COVID-19, induced by the SARS-CoV-2 infection, has caused an unprecedented pandemic in the world. New variants of the virus have emerged and dominated the virus population. In this paper, we develop a multi-strain model with asymptomatic transmission to study how the asymptomatic or pre-symptomatic infection influences the transmission between different strains and control strategies that aim to mitigate the pandemic. Both analytical and numerical results reveal that the competitive exclusion principle still holds for the model with the asymptomatic transmission. By fitting the model to the COVID-19 case and viral variant data in the US, we show that the omicron variants are more transmissible but less fatal than the previously circulating variants. The basic reproduction number for the omicron variants is estimated to be 11.15, larger than that for the previous variants. Using mask mandate as an example of non-pharmaceutical interventions, we show that implementing it before the prevalence peak can significantly lower and postpone the peak. The time of lifting the mask mandate can affect the emergence and frequency of subsequent waves. Lifting before the peak will result in an earlier and much higher subsequent wave. Caution should also be taken to lift the restriction when a large portion of the population remains susceptible. The methods and results obtained her e may be applied to the study of the dynamics of other infectious diseases with asymptomatic transmission using other control measures.

Stochastic SIR model predicts the evolution of COVID-19 epidemics from public health and wastewater data in small and medium-sized municipalities: A one year study

The level of unpredictability of the COVID-19 pandemics poses a challenge to effectively model its dynamic evolution. In this study we incorporate the inherent stochasticity of the SARS-CoV-2 virus spread by reinterpreting the classical compartmental models of infectious diseases (SIR type) as chemical reaction systems modeled via the Chemical Master Equation and solved by Monte Carlo Methods. Our model predicts the evolution of the pandemics at the level of municipalities, incorporating for the first time (i) a variable infection rate to capture the effect of mitigation policies on the dynamic evolution of the pandemics (ii) SIR-with-jumps taking into account the possibility of multiple infections from a single infected person and (iii) data of viral load quantified by RT-qPCR from samples taken from Wastewater Treatment Plants. The model has been successfully employed for the prediction of the COVID-19 pandemics evolution in small and medium size municipalities of Galicia (Northwest of Spain).

A Time-Delayed Deterministic Model for the Spread of COVID-19 with Calibration on a Real Dataset

During the evolution of the COVID-19 pandemic, each country has adopted different control measures to contrast the epidemic’s diffusion. Restrictions to mobility, public transport, and social life in general have been actuated to contain the spread of the pandemic. In this paper, we consider the deterministic SIRD model with delays proposed by (Calleri et al., 2021), which is improved by adding the vaccinated compartment V (SIRDV model) and considering a time-dependent contact frequency. The three delays take into account the incubation time of the disease, the healing time, and the death time. The aim of this work is to study the effect of the vaccination campaigns in Great Britain (GBR) and Israel (ISR) during the pandemic period. The different restriction periods are included by fitting the contact frequency on real datasets as a piecewise constant function. As expected, the vaccination campaign reduces the amount of deaths and infected people. Furthermore, for the different levels of restriction policy, we find specific values of the contact frequency that can be used to predict the trend of the pandemic.