Epidemic models with discrete state structures

The changing economic relationship between some of the major COVID-19 impacted countries with prominent wealth: a comparative study from the view point of stock markets

In the present work, a study has been made over the prime stock indices of some fiscally prominent countries impacted by COVID-19. The countries are separated in two ways: (1) considering gross total number of infected cases-here seven mostly impacted countries with certain global economic influence are selected; (2) considering the concentration of the infected cases-here six major impacted countries with considerable influence are selected. This sort of categorization is itself a novel strategy which is capable of including some less populated, but severely impacted countries of economic importance. The objective of the present analysis is to comprehend the impact of COVID-19 on these markets and to recognize the effect of COVID-19 on mutual association and dependence between these markets. To add more flavour of reliability, we have taken a new and fresh strategy of fixing the time frames under consideration before and during COVID-19 pandemic as uniform. We have used both linear and nonlinear Granger causality analysis and employed generalized forecast error variance decomposition analysis to review the exogeneity and endogeneity of the individual markets. The present study shows that this pandemic has changed the underlying relationship: some exogenous stock markets have become endogenous and vice versa in the pandemic. Linear relationship has been reduced radically, whereas nonlinear relationship has been improved during the COVID-affected period. TASE, the highest returned and significantly uncorrelated index, emerged as the most exogenous market in the pre-COVID period, though it is nonlinearly endogenous in the long term, in the COVD-affected period. CAC 40 is the most endogenous market for the short term in both pre-COVID and COVID-affected period. B3 and NYSE, exogenous in the pre-COVID period, turned out to be linearly endogenous in the COVID-affected duration, whereas BIST 100 and BSE SENSEX are found to be exogenous markets in the COVID-affected period according to both linear and nonlinear causal analysis. They were also exogenous in the pre-COVID era for the short-term period, with BSE SENSEX exhibiting exogeneity anti-persistently for the COVID-affected period too. Association among the markets is more in long term rather than short term. A possible conclusion is also that the markets may regain long-term association once the effect of COVID would fade away.

Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil

This paper compares and contrasts the spread and impact of COVID-19 in the three countries most heavily impacted by the pandemic: the United States (US), India and Brazil. All three of these countries have a federal structure, in which the individual states have largely determined the response to the pandemic. Thus, we perform an extensive analysis of the individual states of these three countries to determine patterns of similarity within each. First, we analyse structural similarity and anomalies in the trajectories of cases and deaths as multivariate time series. Next, we study the lengths of the different waves of the virus outbreaks across the three countries and their states. Finally, we investigate suitable time offsets between cases and deaths as a function of the distinct outbreak waves. In all these analyses, we consistently reveal more characteristically distinct behaviour between US and Indian states, while Brazilian states exhibit less structure in their wave behaviour and changing progression between cases and deaths.

Discrete state-structured epidemic models with distributed delays

In this paper, we propose and investigate a class of discrete state-structured epidemic models with distributed delays. The model incorporates a general delay incidence form in which new infections distribute into different disease states, and infected individuals switch among different states. We establish that the global dynamics are completely determined by basic reproduction number [Formula: see text]: if [Formula: see text], the disease free equilibrium is globally asymptotically stable; if [Formula: see text], the disease free equilibrium is unstable, and there is a unique endemic equilibrium which is globally asymptotically stable.

Estimating a continuously varying offset between multivariate time series with application to COVID-19 in the United States

This paper introduces new methods to track the offset between two multivariate time series on a continuous basis. We then apply this framework to COVID-19 counts on a state-by-state basis in the United States to determine the progression from cases to deaths as a function of time. Across multiple approaches, we reveal an "up-down-up" pattern in the estimated offset between reported cases and deaths as the pandemic progresses. This analysis could be used to predict imminent increased load on a healthcare system and aid the allocation of additional resources in advance.

Trends in COVID-19 prevalence and mortality: A year in review

This paper introduces new methods to study the changing dynamics of COVID-19 cases and deaths among the 50 worst-affected countries throughout 2020. First, we analyse the trajectories and turning points of rolling mortality rates to understand at which times the disease was most lethal. We demonstrate five characteristic classes of mortality rate trajectories and determine structural similarity in mortality trends over time. Next, we introduce a class of virulence matrices to study the evolution of COVID-19 cases and deaths on a global scale. Finally, we introduce three-way inconsistency analysis to determine anomalous countries with respect to three attributes: countries' COVID-19 cases, deaths and human development indices. We demonstrate the most anomalous countries across these three measures are Pakistan, the United States and the United Arab Emirates.

Nonlinear science against the COVID-19 pandemic

This special issue showcases recent uses of mathematical and nonlinear science methods in the study of different problems arising in the context of the COVID-19 pandemic. The sixteen original research papers included in this collection span a wide spectrum of studies including classical epidemiological models, new models accounting for COVID-19 specificities, non-pharmaceutical control measures, network models and other problems related to the pandemic.