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Register a new userEpidemic spreading in an expanded parameter space: the supercritical scaling laws and subcritical metastable phases
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So far most of the analysis of coronavirus 2020 epidemic data has been focusing on a short-time window and consequently a quantitative test of statistical physical laws of Coronavirus Epidemics with Containment Measures (CEwCM) is currently lacking. Here we report a quantitative analysis of CEwCM over 230 days, covering the full-time lapse of the first epidemic wave. We use a 3D phase diagram tracking the simultaneous evolution of the doubling time Td(t) and reproductive number Rt(t) showing that this expanded parameter space is needed for biological physics of CEwCP. We have verified that in the supercritical [Rt(t)>1, Td(t)<40 days] regime i) the curve Z(t) of total infected cases follows the growth rate called Ostwald law; ii) the doubling time follows the exponential law Td(t)=A exp((t-t0)/s) as a function of time and iii) the power law Td(t)=C(Rt(t)-1)^-n is verified with the exponent n depending on the definition of Rt(t). The log-log plots Td(t) versus (Rt-1) of the second 2020 epidemic wave unveil in the subcritical regime [Td(t)>100 days] arrested metastable phases with Rt>1 where Td(t) was kept constant followed by its explosion and its containment following the same power law as in the first wave
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Understanding and predicting outbreaks of contagious diseases are crucial to the development of society and public health, especially for underdeveloped countries. However, challenging problems are encountered because of complex epidemic spreading dynamics influenced by spatial structure and human dynamics (including both human mobility and human interaction intensity). We propose a systematical model to depict nationwide epidemic spreading in C^{o}te dIvoire, which integrates multiple factors, such as human mobility, human interaction intensity, and demographic features. We provide insights to aid in modeling and predicting the epidemic spreading process by data-driven simulation and theoretical analysis, which is otherwise beyond the scope of local evaluation and geometrical views. We show that the requirement that the average local basic reproductive number to be greater than unity is not necessary for outbreaks of epidemics. The observed spreading phenomenon can be roughly explained as a heterogeneous diffusion-reaction process by redefining mobility distance according to the human mobility volume between nodes, which is beyond the geometrical viewpoint. However, the heterogeneity of human dynamics still poses challenges to precise prediction.
Macroscopic growth laws, solutions of mean field equations, describe in an effective way an underlying complex dynamics. They are applied to study the spreading of infections, as in the case of CoviD-19, where the counting of the cumulated number $N(t)$ of detected infected individuals is a generally accepted, coarse-grain, variable to understand the epidemic phase. However $N(t)$ does not take into account the unknown number of asymptomatic, not detected, cases $A(t)$. Therefore, the question arises if the observed time series of data of $N(t)$ is a reliable tool for monitoring the evolution of the infectious disease. We study a system of coupled differential equations which includes the dynamics of the spreading among symptomatic and asymptomatic individuals and the strong containment effects due to the social isolation. The solution is therefore compared with a macroscopic law for the population $N(t)$ coming from a single, non-linear, differential equation with no explicit reference to $A(t)$, showing the equivalence of the two methods. Indeed, $N(t)$ takes into account a more complex and detailed population dynamics which permits the evaluation of the number of asymptomatic individuals also. The model is then applied to Covid-19 spreading in Italy where a transition from an exponential behavior to a Gompertz growth for $N(t)$ has been observed in more recent data. Then the information contained in the data analysis of $N(t)$ is reliable to understand the epidemic phase, although it does not describe the total infected population. The asymptomatic population is larger than the symptomatic one in the fast growth phase of the spreading.
The control of Covid 19 epidemics by public health policy in Italy during the first and the second epidemic waves has been driven by using reproductive number Rt(t) to identify the supercritical (percolative), the subcritical (arrested), separated by the critical regime. Here we show that to quantify the Covid-19 spreading rate with containment measures (CSRwCM) there is a need of a 3D expanded parameter space phase diagram built by the combination of Rt(t) and doubling time Td(t). In this space we identify the dynamics of the Covid-19 dynamics Italy and its administrative Regions. The supercritical regime is mathematically characterized by i) the power law of Td vs. [Rt(t)-1] and ii) the exponential behaviour of Td vs. time, either in the first and in the second wave. The novel 3D phase diagram shows clearly metastable states appearing before and after the second wave critical regime. for loosening quarantine and tracing of actives cases. The metastable states are precursors of the abrupt onset of a next nascent wave supercritical regime. This dynamic description allows epidemics predictions needed by policymakers to activate non-pharmaceutical interventions (NPIs), a key issue for avoiding economical losses, reduce fatalities and avoid new virus variant during vaccination campaign
The COVID-19 pandemic has challenged authorities at different levels of government administration around the globe. When faced with diseases of this severity, it is useful for the authorities to have prediction tools to estimate in advance the impact on the health system and the human, material, and economic resources that will be necessary. In this paper, we construct an extended Susceptible-Exposed-Infected-Recovered model that incorporates the social structure of Mar del Plata, the $4^circ$ most inhabited city in Argentina and head of the Municipality of General Pueyrredon. Moreover, we consider detailed partitions of infected individuals according to the illness severity, as well as data of local health resources, to bring these predictions closer to the local reality. Tuning the corresponding epidemic parameters for COVID-19, we study an alternating quarantine strategy, in which a part of the population can circulate without restrictions at any time, while the rest is equally divided into two groups and goes on successive periods of normal activity and lockdown, each one with a duration of $tau$ days. Besides, we implement a random testing strategy over the population. We found that $tau = 7$ is a good choice for the quarantine strategy since it matches with the weekly cycle as it reduces the infected population. Focusing on the health system, projecting from the situation as of September 30, we foresee a difficulty to avoid saturation of ICU, given the extremely low levels of mobility that would be required. In the worst case, our model estimates that four thousand deaths would occur, of which 30% could be avoided with proper medical attention. Nonetheless, we found that aggressive testing would allow an increase in the percentage of people that can circulate without restrictions, being the equipment required to deal with the additional critical patients relatively low.
Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. Here, we introduce a disease model with an underlying genotype network to account for two important mechanisms. One, the disease can mutate along network pathways as it spreads in a host population. Two, the genotype network allows us to define a genetic distance across strains and therefore to model the transcendence of immunity often observed in real world pathogens. We study the emergence of epidemics in this model, through its epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases, large scale fluctuations, sequential epidemic transitions, as well as localization around specific strains of the associated pathogen. More generally, our model illustrates the richness of behaviours that are possible even in well-mixed host populations once we consider strain diversity and go beyond the one disease equals one pathogen paradigm.
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