We formulate a compartmental model for the propagation of a respiratory disease in a patchy environment. The patches are connected through the mobility of individuals, and we assume that disease transmission and recovery are possible during travel. Moreover, the migration terms are assumed to depend on the distance between patches and the perceived severity of the disease. The positivity and boundedness of the model solutions are discussed. We analytically show the existence and global asymptotic stability of the disease-free equilibrium. We study three different network topologies numerically and find that underlying network structure is crucial for disease transmission. Further numerical simulations reveal that infection during travel has the potential to change the stability of disease-free equilibrium from stable to unstable. The coupling strength and transmission coefficients are also very crucial in disease propagation. Different exit screening scenarios indicate that the patch with the highest prevalence may have adverse effects but other patches will be benefited from exit screening. Furthermore, while studying the multi-strain dynamics, it is observed that two co-circulating strains will not persist simultaneously in the community but only one of the strains may persist in the long run. Transmission coefficients corresponding to the second strain are very crucial and show threshold like behavior with respect to the equilibrium density of the second strain.
Spatiotemporal fluctuation scaling law and metapopulation modeling of the novel coronavirus (COVID-19) and SARS outbreaks
我们对比分析了2019年新型冠状病毒（COVID-19）和SARS疫情的时空波动，以了解其流行病学特征。在方法上，我们引入TPL（泰勒幂律）来表征其时空异质性/稳定性，并引入Hubbell（2001）生物多样性统一中性学说〈动〉<动>（UNTB）[特别是Harris et al.（2015）HDP-MSN模型（分层狄利克雷过程多位点中性模型）]来近似冠状病毒感染的集合种群。首先，TPL分析表明，冠状病毒似乎具有特定的异质性/稳定性缩放参数（TPL-b），对于累积感染略大于2，对于每日增量感染略大于1，这表明它们可能是混乱的，不稳定的爆发。另一TPL参数（M0）（即，感染临界阈值）取决于病毒种类（COVID-19/SARS）、时间（疾病阶段）、空间（区域）和公共卫生干预（例如，移动性和移动性控制）。M0测量感染水平，在该感染水平下感染是随机的（泊松分布），低于该感染水平的感染遵循均匀分布，如果M0符合或低于Allee效应水平，则可能会死亡。研究发现，COVID-19爆发的风险似乎比SARS高出近两倍，而较低的感染阈值可能是由于其致死率低于SARS，因为较低的致死率可以促进病原体的存活和传播。第二，后趋性UNTB中性测试似乎适合于近似冠状病毒感染的后趋性。具体而言，从中性学说〈动〉<动>中借用的两个参数θ和M可用于评估通过局部传染感染与通过迁移感染的相对重要性，这两者都可能取决于时间、…
Computational models of infectious disease can be broadly categorized into two types: individual-based (Agent-based), or compartmental models. While compartmental models can be structured to separate distinct sectors of a population, they are conceptually distinct from individual-based models in which population structure emerges from micro-scale interactions. While the conceptual distinction is straightforward, a fair comparison of the approaches is difficult to achieve. Here, we carry out such a comparison by building a set of compartmental metapopulation models from an agent-based represent…
The Covid-19 pandemic has taken millions of lives, demonstrating the tragedy and disruption of respiratory diseases, and how difficult they can be to manage. However, there is still significant debate in the scientific community as to which transmission pathways are most significant and how settings and behaviour affect risk of infection, which all have implications for which mitigation strategies are most effective. This study presents a general model to estimate the rate of viral transfer between individuals, objects, and the air. The risk of infection to individuals in a setting is then com…
In this article, we develop a simple mathematical GNU Octave/MATLAB code that is easy to modify for the simulation of mathematical models governed by fractional-order differential equations, and for the resolution of fractional-order optimal control problems through Pontryagin's maximum principle (indirect approach to optimal control). For this purpose, a fractional-order model for the respiratory syncytial virus (RSV) infection is considered. The model is an improvement of one first proposed by the authors in [Chaos Solitons Fractals 117 (2018), 142--149]. The initial value problem associated…
Respiratory syncytial virus (RSV) is a leading cause of acute lower respiratory tract infection worldwide, resulting in approximately sixty thousand annual hospitalizations of <5-year-olds in the United States alone and three million annual hospitalizations globally. The development of over 40 vaccines and immunoprophylactic interventions targeting RSV has the potential to significantly reduce the disease burden from RSV infection in the near future. In the context of RSV, a highly contagious pathogen, dynamic transmission models (DTMs) are valuable tools in the evaluation and comparison of th…
Mathematical models of SARS-CoV-2 spread are used for guiding the design of mitigation steps aimed at containing and decelerating the contagion, and at identifying impending breaches of health care system surge capacity. The challenges of having only lacunary information about daily new infections are compounded by the geographic heterogeneity of the population. To address this problem, we propose to account for the differences between rural and urban settings using network-based, distributed models where the spread of the pandemic is described in distinct local cohorts with nested SEIR models…
Inference for stochastic kinetic models from multiple data sources for joint estimation of infection dynamics from aggregate reports and virological data
We quantified the probability of developing symptoms (respiratory or fever \geq 37.5 °C) and critical disease (requiring intensive care or resulting in death) of SARS-CoV-2 positive subjects. 5,484 contacts of SARS-CoV-2 index cases detected in Lombardy, Italy were analyzed, and positive subjects were ascertained via nasal swabs and serological assays. 73.9% of all infected individuals aged less than 60 years did not develop symptoms (95% confidence interval: 71.8-75.9%). The risk of symptoms increased with age. 6.6% of infected subjects older than 60 years had critical disease, with males at …
Identifying the relative importance of the different transmission routes of the SARS-CoV-2 virus is an urgent research priority. To that end, the different transmission routes, and their role in determining the evolution of the Covid-19 pandemic are analyzed in this work. Probability of infection caused by inhaling virus-laden droplets (initial, ejection diameters between $0.5-750μm$) and the corresponding desiccated nuclei that mostly encapsulate the virions post droplet evaporation, are individually calculated. At typical, air-conditioned yet quiescent indoor space, for average viral loading…
After the detection of coronavirus disease 2019 (Covid-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Wuhan, Hubei Province, China in late December, the cases of Covid-19 have spiralled out around the globe. Due to the clinical similarity of Covid-19 with other flulike syndromes, patients are assayed for other pathogens of influenza like illness. There have been reported cases of co-infection amongst patients with Covid-19. Bacteria for example Streptococcus pneumoniae, Staphylococcus aureus, Klebsiella pneumoniae, Mycoplasma pneumoniae, Chlamydia pneumonia,…
In this study, we apply a novel combination of close proximity and room-scale risk assessment approaches for people sharing public transport environments to predict their contagion risk due to SARS-CoV-2 respiratory infection. In particular, the individual infection risk of susceptible subjects and the transmissibility of SARS-CoV-2 (expressed through the reproduction number) are evaluated for two types of buses, differing in terms of exposure time and crowding index: urban and long-distance buses. Infection risk and reproduction number are calculated for different scenarios as a function of t…
Disease outbreaks, such as those of Severe Acute Respiratory Syndrome in 2003 and the 2009 pandemic A(H1N1) influenza, have highlighted the potential for airborne transmission in indoor environments. Respirable pathogen-carrying droplets provide a vector for the spatial spread of infection with droplet transport determined by diffusive and convective processes. An epidemiological model describing the spatial dynamics of disease transmission is presented. The effects of an ambient airflow, as an infection control, are incorporated leading to a delay equation, with droplet density dependent on t…
Coronavirus disease 2019 (COVID-19) is a continuously devastating public health and the world economy. One of the major challenges in controlling the COVID-19 outbreak is its asymptomatic infection and transmission, which are elusive and defenseless in most situations. The pathogenicity and virulence of asymptomatic COVID-19 remain mysterious. Based on the genotyping of 20656 Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) genome isolates, we reveal that asymptomatic infection is linked to SARS-CoV-2 11083G>T mutation, i.e., leucine (L) to phenylalanine (F) substitution at the res…
Contagious respiratory diseases, such as COVID-19, depend on sufficiently prolonged exposures for the successful transmission of the underlying pathogen. It is important for organizations to evaluate the efficacy of interventions aiming at mitigating viral transmission among their personnel. We have developed a operational risk assessment simulation framework that couples a spatial agent-based model of movement with a SIR epidemiological model to assess the relative risks of different intervention strategies. By applying our model on MIT's STATA building, we assess the impacts of three possibl…
The outbreak of a novel coronavirus causing severe acute respiratory syndrome in December 2019 has escalated into a worldwide pandemic. In this work, we propose a compartmental model to describe the dynamics of transmission of infection and use it to obtain the optimal vaccination control. The model accounts for the various stages of the vaccination and the optimisation is focused on minimising the infections to protect the population and relieve the healthcare system. As a case study we selected the Republic of Ireland. We use data provided by Ireland's COVID-19 Data-Hub and simulate the evol…
