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1.
Bull Math Biol ; 84(6): 66, 2022 May 13.
Article in English | MEDLINE | ID: covidwho-1844446

ABSTRACT

Testing individuals for pathogens can affect the spread of epidemics. Understanding how individual-level processes of sampling and reporting test results can affect community- or population-level spread is a dynamical modeling question. The effect of testing processes on epidemic dynamics depends on factors underlying implementation, particularly testing intensity and on whom testing is focused. Here, we use a simple model to explore how the individual-level effects of testing might directly impact population-level spread. Our model development was motivated by the COVID-19 epidemic, but has generic epidemiological and testing structures. To the classic SIR framework we have added a per capita testing intensity, and compartment-specific testing weights, which can be adjusted to reflect different testing emphases-surveillance, diagnosis, or control. We derive an analytic expression for the relative reduction in the basic reproductive number due to testing, test-reporting and related isolation behaviours. Intensive testing and fast test reporting are expected to be beneficial at the community level because they can provide a rapid assessment of the situation, identify hot spots, and may enable rapid contact-tracing. Direct effects of fast testing at the individual level are less clear, and may depend on how individuals' behaviour is affected by testing information. Our simple model shows that under some circumstances both increased testing intensity and faster test reporting can reduce the effectiveness of control, and allows us to explore the conditions under which this occurs. Conversely, we find that focusing testing on infected individuals always acts to increase effectiveness of control.


Subject(s)
COVID-19 , Epidemics , COVID-19/diagnosis , COVID-19/epidemiology , Epidemics/prevention & control , Humans , Mathematical Concepts , Models, Biological , SARS-CoV-2
2.
Bull Math Biol ; 84(6): 63, 2022 May 04.
Article in English | MEDLINE | ID: covidwho-1824785

ABSTRACT

We extended a class of coupled PDE-ODE models for studying the spatial spread of airborne diseases by incorporating human mobility. Human populations are modeled with patches, and a Lagrangian perspective is used to keep track of individuals' places of residence. The movement of pathogens in the air is modeled with linear diffusion and coupled to the SIR dynamics of each human population through an integral of the density of pathogens around the population patches. In the limit of fast diffusion pathogens, the method of matched asymptotic analysis is used to reduce the coupled PDE-ODE model to a nonlinear system of ODEs for the average density of pathogens in the air. The reduced system of ODEs is used to derive the basic reproduction number and the final size relation for the model. Numerical simulations of the full PDE-ODE model and the reduced system of ODEs are used to assess the impact of human mobility, together with the diffusion of pathogens on the dynamics of the disease. Results from the two models are consistent and show that human mobility significantly affects disease dynamics. In addition, we show that an increase in the diffusion rate of pathogen leads to a lower epidemic.


Subject(s)
Communicable Diseases , Epidemics , Basic Reproduction Number , Communicable Diseases/epidemiology , Diffusion , Humans , Mathematical Concepts , Models, Biological
3.
Bull Math Biol ; 84(5): 57, 2022 Apr 08.
Article in English | MEDLINE | ID: covidwho-1782924

ABSTRACT

Accurate prediction of the number of daily or weekly confirmed cases of COVID-19 is critical to the control of the pandemic. Existing mechanistic models nicely capture the disease dynamics. However, to forecast the future, they require the transmission rate to be known, limiting their prediction power. Typically, a hypothesis is made on the form of the transmission rate with respect to time. Yet the real form is too complex to be mechanistically modeled due to the unknown dynamics of many influential factors. We tackle this problem by using a hypothesis-free machine-learning algorithm to estimate the transmission rate from data on non-pharmaceutical policies, and in turn forecast the confirmed cases using a mechanistic disease model. More specifically, we build a hybrid model consisting of a mechanistic ordinary differential equation (ODE) model and a gradient boosting model (GBM). To calibrate the parameters, we develop an "inverse method" that obtains the transmission rate inversely from the other variables in the ODE model and then feed it into the GBM to connect with the policy data. The resulting model forecasted the number of daily confirmed cases up to 35 days in the future in the USA with an averaged mean absolute percentage error of 27%. It can identify the most informative predictive variables, which can be helpful in designing improved forecasters as well as informing policymakers.


Subject(s)
COVID-19 , COVID-19/epidemiology , COVID-19/prevention & control , Humans , Machine Learning , Mathematical Concepts , Models, Biological , Pandemics/prevention & control
4.
Bull Math Biol ; 84(5): 55, 2022 Apr 04.
Article in English | MEDLINE | ID: covidwho-1772996

ABSTRACT

The sudden outbreak of SARS-CoV-2 has caused the shortage of medical resources around the world, especially in developing countries and underdeveloped regions. With the continuous increase in the duration of this disease, the control of migration of humans between regions or countries has to be relaxed. Based on this, we propose a two-patches mathematical model to simulate the transmission of SARS-CoV-2 among two-patches, asymptomatic infected humans and symptomatic infected humans, where a half-saturated detection rate function is also introduced to describe the effect of medical resources. By applying the methods of linearization and constructing a suitable Lyapunov function, the local and global stability of the disease-free equilibrium of this model without migration is obtained. Further, the existence of forward/backward bifurcation is analyzed, which is caused by the limited medical resources. This means that the elimination or prevalence of the disease no longer depends on the basic reproduction number but is closely related to the initial state of asymptomatic and symptomatic infected humans and the supply of medical resources. Finally, the global dynamics of the full model are discussed, and some numerical simulations are carried to explain the main results and the effects of migration and supply of medical resources on the transmission of disease.


Subject(s)
COVID-19 , SARS-CoV-2 , Basic Reproduction Number , COVID-19/epidemiology , Humans , Mathematical Concepts , Models, Biological
5.
Bull Math Biol ; 84(4): 44, 2022 02 17.
Article in English | MEDLINE | ID: covidwho-1694335

ABSTRACT

A widely used tool for analysing the Covid-19 pandemic is the standard SIR model. It seems often to be used as a black box, not taking into account that this model was derived as a special case of the seminal Kermack-McKendrick theory from 1927. This is our starting point. We explain the setup of the Kermack-McKendrick theory (passing to a discrete approach) and use medical information for specializing to a model called by us an adapted K-McK-model. It includes effects of vaccination, mass testing and mutants. We demonstrate the use of the model by applying it to the development in Germany and show, among others things, that a comparatively mild intervention reducing the time until quarantine by one day would lead to a drastic improvement.


Subject(s)
COVID-19 , Humans , Mathematical Concepts , Models, Biological , Pandemics , SARS-CoV-2
6.
Bull Math Biol ; 84(3): 38, 2022 Feb 07.
Article in English | MEDLINE | ID: covidwho-1681662

ABSTRACT

To uncover the effective interventions during the pandemic period, a novel mathematical model, which incorporates separate compartments for incubation and asymptomatic individuals, has been developed in this paper. On the basis of a general mixing, final size relation and next-generation matrix are derived for a meta-population model by introducing the matrix blocking. The final size ([Formula: see text]) and the basic reproduction number ([Formula: see text]) are no longer a simple monotonous relationship. The analytical results of heterogeneity illustrate that activity is more sensitive than the others. And the proportion of asymptomatic individuals is a key factor for final epidemic size compared to the regulatory factor. Furthermore, the impact of preferential contact level on [Formula: see text] and [Formula: see text] is comparatively complex. The isolation can effectively reduce the final size, which further verifies its effectiveness. When vaccination is considered, the mixing methods maybe influence the doses of vaccination used and its effective. Moreover, using the present predictive model, we can provide the valuable reference about identifying the ideal strategies to curb the pandemic disease.


Subject(s)
Mathematical Concepts , Models, Biological , Basic Reproduction Number , Humans , Pandemics/prevention & control , Vaccination
7.
Bull Math Biol ; 84(3): 32, 2022 01 24.
Article in English | MEDLINE | ID: covidwho-1653712

ABSTRACT

The COVID-19 pandemic has had a considerable impact on global health and economics. The impact in African countries has not been investigated thoroughly via fitting epidemic models to the reported COVID-19 deaths. We downloaded the data for the 12 most-affected countries with the highest cumulative COVID-19 deaths to estimate the time-varying basic reproductive number ([Formula: see text]) and infection attack rate. We develop a simple epidemic model and fitted it to reported COVID-19 deaths in 12 African countries using iterated filtering and allowing a flexible transmission rate. We observe high heterogeneity in the case-fatality rate across the countries, which may be due to different reporting or testing efforts. South Africa, Tunisia, and Libya were most affected, exhibiting a relatively higher [Formula: see text] and infection attack rate. Thus, to effectively control the spread of COVID-19 epidemics in Africa, there is a need to consider other mitigation strategies (such as improvements in socioeconomic well-being, healthcare systems, the water supply, and awareness campaigns).


Subject(s)
COVID-19 , Pandemics , Humans , Mathematical Concepts , Models, Biological , SARS-CoV-2 , South Africa
8.
Comput Math Methods Med ; 2022: 7772263, 2022.
Article in English | MEDLINE | ID: covidwho-1625636

ABSTRACT

COVID-19 is a world pandemic that has affected and continues to affect the social lives of people. Due to its social and economic impact, different countries imposed preventive measures that are aimed at reducing the transmission of the disease. Such control measures include physical distancing, quarantine, hand-washing, travel and boarder restrictions, lockdown, and the use of hand sanitizers. Quarantine, out of the aforementioned control measures, is considered to be more stressful for people to manage. When people are stressed, their body immunity becomes weak, which leads to multiplying of coronavirus within the body. Therefore, a mathematical model consisting of six compartments, Susceptible-Exposed-Quarantine-Infectious-Hospitalized-Recovered (SEQIHR) was developed, aimed at showing the impact of stress on the transmission of COVID-19 disease. From the model formulated, the positivity, bounded region, existence, uniqueness of the solution, the model existence of free and endemic equilibrium points, and local and global stability were theoretically proved. The basic reproduction number (R 0) was derived by using the next-generation matrix method, which shows that, when R 0 < 1, the disease-free equilibrium is globally asymptotically stable whereas when R 0 > 1 the endemic equilibrium is globally asymptotically stable. Moreover, the Partial Rank Correlation Coefficient (PRCC) method was used to study the correlation between model parameters and R 0. Numerically, the SEQIHR model was solved by using the Rung-Kutta fourth-order method, while the least square method was used for parameter identifiability. Furthermore, graphical presentation revealed that when the mental health of an individual is good, the body immunity becomes strong and hence minimizes the infection. Conclusively, the control parameters have a significant impact in reducing the transmission of COVID-19.


Subject(s)
COVID-19/epidemiology , COVID-19/prevention & control , Pandemics/prevention & control , Quarantine , SARS-CoV-2 , Stress, Physiological , Basic Reproduction Number/statistics & numerical data , COVID-19/physiopathology , Computational Biology , Computer Simulation , Humans , Mathematical Concepts , Models, Statistical , Pandemics/statistics & numerical data , Quarantine/psychology , Stress, Psychological
9.
Bull Math Biol ; 84(2): 30, 2022 01 10.
Article in English | MEDLINE | ID: covidwho-1616222

ABSTRACT

The COVID-19 pandemic has adversely affected the entire world. The effective implementation of vaccination strategy is critical to prevent the resurgence of the pandemic, especially during large-scale population migration. We establish a multiple patch coupled model based on the transportation network among the 31 provinces in China, under the combined strategies of vaccination and quarantine during large-scale population migration. Based on the model, we derive a critical quarantine rate to control the pandemic transmission and a vaccination rate to achieve herd immunity. Furthermore, we evaluate the influence of passenger flow on the effective reproduction number during the Chinese-Spring-Festival travel rush. Meanwhile, the spread of the COVID-19 pandemic is investigated for different control strategies, viz. global control and local control. The impact of vaccine-related parameters, such as the number, the effectiveness and the immunity period of vaccine, are explored. It is believed that the articulated models as well as the presented simulation results could be beneficial to design of feasible strategies for preventing COVID-19 transmission during the Chinese-Spring-Festival travel rush or the other future events involving large-scale population migration.


Subject(s)
COVID-19 , Quarantine , China/epidemiology , Holidays , Humans , Mathematical Concepts , Models, Biological , Pandemics/prevention & control , SARS-CoV-2 , Travel , Vaccination
10.
Bull Math Biol ; 84(2): 28, 2022 01 04.
Article in English | MEDLINE | ID: covidwho-1608940

ABSTRACT

The spread of COVID-19 in Wuhan was successfully curbed under the strategy of "Joint Prevention and Control Mechanism." To understand how this measure stopped the epidemics in Wuhan, we establish a compartmental model with time-varying parameters over different stages. In the early stage of the epidemic, due to resource limitations, the number of daily reported cases may lower than the actual number. We employ a dynamic-based approach to calibrate the accumulated clinically diagnosed data with a sudden jump on February 12 and 13. The model simulation shows reasonably good match with the adjusted data which allows the prediction of the cumulative confirmed cases. Numerical results reveal that the "Joint Prevention and Control Mechanism" played a significant role on the containment of COVID-19. The spread of COVID-19 cannot be inhibited if any of the measures was not effectively implemented. Our analysis also illustrates that the Fangcang Shelter Hospitals are very helpful when the beds in the designated hospitals are insufficient. Comprised with Fangcang Shelter Hospitals, the designated hospitals can contain the transmission of COVID-19 more effectively. Our findings suggest that the combined multiple measures are essential to curb an ongoing epidemic if the prevention and control measures can be fully implemented.


Subject(s)
COVID-19 , China/epidemiology , Humans , Mathematical Concepts , Models, Biological , SARS-CoV-2
11.
Bull Math Biol ; 84(2): 27, 2022 01 04.
Article in English | MEDLINE | ID: covidwho-1602877

ABSTRACT

Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development. Thus the value of understanding the impact of immunological parameters on epidemiological quantities. Here we consider an age-since-infection structured vector-host model, in which epidemiological parameters are formulated as functions of within-host virus and antibody densities, governed by an ODE system. We then use SA for these immuno-epidemiological models to investigate the impact of immunological parameters on population-level disease dynamics such as basic reproduction number, final size of the epidemic or the infectiousness at different phases of an outbreak. As a case study, we consider Rift Valley Fever Disease utilizing parameter estimations from prior studies. SA indicates that [Formula: see text] increase in within-host pathogen growth rate can lead up to [Formula: see text] increase in [Formula: see text] up to [Formula: see text] increase in steady-state infected host abundance, and up to [Formula: see text] increase in infectiousness of hosts when the reproduction number [Formula: see text] is larger than one. These significant increases in population-scale disease quantities suggest that control strategies that reduce the within-host pathogen growth can be important in reducing disease prevalence.


Subject(s)
Models, Biological , Rift Valley Fever , Animals , Basic Reproduction Number , Disease Vectors , Mathematical Concepts
12.
Bull Math Biol ; 84(1): 3, 2021 11 19.
Article in English | MEDLINE | ID: covidwho-1525588

ABSTRACT

The COVID-19 pandemic has placed epidemiologists, modelers, and policy makers at the forefront of the global discussion of how to control the spread of coronavirus. The main challenges confronting modelling approaches include real-time projections of changes in the numbers of cases, hospitalizations, and fatalities, the consequences of public health policy, the understanding of how best to implement varied non-pharmaceutical interventions and potential vaccination strategies, now that vaccines are available for distribution. Here, we: (i) review carefully selected literature on COVID-19 modeling to identify challenges associated with developing appropriate models along with collecting the fine-tuned data, (ii) use the identified challenges to suggest prospective modeling frameworks through which adaptive interventions such as vaccine strategies and the uses of diagnostic tests can be evaluated, and (iii) provide a novel Multiresolution Modeling Framework which constructs a multi-objective optimization problem by considering relevant stakeholders' participatory perspective to carry out epidemic nowcasting and future prediction. Consolidating our understanding of model approaches to COVID-19 will assist policy makers in designing interventions that are not only maximally effective but also economically beneficial.


Subject(s)
COVID-19 , Pandemics , Humans , Mathematical Concepts , Prospective Studies , SARS-CoV-2
13.
PLoS Comput Biol ; 17(10): e1009473, 2021 10.
Article in English | MEDLINE | ID: covidwho-1496327

ABSTRACT

Infectious diseases attack humans from time to time and threaten the lives and survival of people all around the world. An important strategy to prevent the spatial spread of infectious diseases is to restrict population travel. With the reduction of the epidemic situation, when and where travel restrictions can be lifted, and how to organize orderly movement patterns become critical and fall within the scope of this study. We define a novel diffusion distance derived from the estimated mobility network, based on which we provide a general model to describe the spatiotemporal spread of infectious diseases with a random diffusion process and a deterministic drift process of the population. We consequently develop a multi-source data fusion method to determine the population flow in epidemic areas. In this method, we first select available subregions in epidemic areas, and then provide solutions to initiate new travel flux among these subregions. To verify our model and method, we analyze the multi-source data from mainland China and obtain a new travel flux triggering scheme in the selected 29 cities with the most active population movements in mainland China. The testable predictions in these selected cities show that reopening the borders in accordance with our proposed travel flux will not cause a second outbreak of COVID-19 in these cities. The finding provides a methodology of re-triggering travel flux during the weakening spread stage of the epidemic.


Subject(s)
COVID-19/epidemiology , Epidemics , SARS-CoV-2 , Travel , COVID-19/prevention & control , COVID-19/transmission , China/epidemiology , Cities , Computational Biology , Humans , Mathematical Concepts , Models, Biological , Spatio-Temporal Analysis , Travel/statistics & numerical data
14.
Comput Math Methods Med ; 2021: 1250129, 2021.
Article in English | MEDLINE | ID: covidwho-1398741

ABSTRACT

We formulate and theoretically analyze a mathematical model of COVID-19 transmission mechanism incorporating vital dynamics of the disease and two key therapeutic measures-vaccination of susceptible individuals and recovery/treatment of infected individuals. Both the disease-free and endemic equilibrium are globally asymptotically stable when the effective reproduction number R 0(v) is, respectively, less or greater than unity. The derived critical vaccination threshold is dependent on the vaccine efficacy for disease eradication whenever R 0(v) > 1, even if vaccine coverage is high. Pontryagin's maximum principle is applied to establish the existence of the optimal control problem and to derive the necessary conditions to optimally mitigate the spread of the disease. The model is fitted with cumulative daily Senegal data, with a basic reproduction number R 0 = 1.31 at the onset of the epidemic. Simulation results suggest that despite the effectiveness of COVID-19 vaccination and treatment to mitigate the spread of COVID-19, when R 0(v) > 1, additional efforts such as nonpharmaceutical public health interventions should continue to be implemented. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. Results shown graphically could help to inform the process of prioritizing public health intervention measures to be implemented and which model parameter to focus on in order to mitigate the spread of the disease. The effective contact rate b, the vaccine efficacy ε, the vaccination rate v, the fraction of exposed individuals who develop symptoms, and, respectively, the exit rates from the exposed and the asymptomatic classes σ and ϕ are the most impactful parameters.


Subject(s)
COVID-19/prevention & control , COVID-19/transmission , Models, Biological , Basic Reproduction Number/statistics & numerical data , COVID-19/therapy , COVID-19 Vaccines/pharmacology , Computer Simulation , Humans , Mathematical Concepts , Nonlinear Dynamics , Pandemics/prevention & control , Pandemics/statistics & numerical data , Public Health , SARS-CoV-2 , Senegal/epidemiology , Vaccination
15.
Comput Math Methods Med ; 2021: 8873059, 2021.
Article in English | MEDLINE | ID: covidwho-1362017

ABSTRACT

When encountering the outbreak and early spreading of COVID-19, the Government of Japan imposed gradually upgraded restriction policies and declared the state of emergency in April 2020 for the first time. To evaluate the efficacy of the countering strategies in different periods, we constructed a SEIADR (susceptible-exposed-infected-asymptomatic-documented-recovered) model to simulate the cases and determined corresponding spreading coefficients. The effective reproduction number R t was obtained to evaluate the measures controlling the COVID-19 conducted by the Government of Japan during different stages. It was found that the strict containing strategies during the state of emergency period drastically inhibit the COVID-19 trend. R t was decreased to 1.1123 and 0.8911 in stages 4 and 5 (a state of emergency in April and May 2020) from 3.5736, 2.0126, 3.0672 in the previous three stages when the containing strategies were weak. The state of emergency was declared again in view of the second wave of massive infections in January 2021. We estimated the cumulative infected cases and additional days to contain the COVID-19 transmission for the second state of emergency using this model. R t was 1.028 which illustrated that the strategies were less effective than the previous state of emergency. Finally, the overall infected population was predicted using combined isolation and testing intensity; the effectiveness and the expected peak time were evaluated. If using the optimized control strategies in the current stage, the spread of COVID-19 in Japan could be controlled within 30 days. The total confirmed cases should reduce to less than 4.2 × 105 by April 2021. This model study suggested stricter isolating measures may be required to shorten the period of the state of emergency.


Subject(s)
COVID-19/epidemiology , COVID-19/transmission , Emergencies , Models, Biological , Pandemics , SARS-CoV-2 , Algorithms , COVID-19/prevention & control , COVID-19 Testing/methods , COVID-19 Testing/statistics & numerical data , Communicable Disease Control/legislation & jurisprudence , Communicable Disease Control/methods , Communicable Disease Control/statistics & numerical data , Computational Biology , Computer Simulation , Humans , Japan/epidemiology , Least-Squares Analysis , Mathematical Concepts , Models, Statistical , National Health Programs/legislation & jurisprudence , Nonlinear Dynamics , Pandemics/prevention & control , Pandemics/statistics & numerical data
16.
Comput Math Methods Med ; 2021: 8924293, 2021.
Article in English | MEDLINE | ID: covidwho-1356985

ABSTRACT

In recent years, with the acceleration of industrialization, urbanization, and aging process, the number of patients with chronic diseases in the world is increasing year by year. In China, the number of chronic diseases has increased tenfold in 10 years. The percentage of the disease burden in the whole society accounts for 79.4%. Chronic diseases have become the top killer for Chinese people's health. However, for chronic diseases, prevention is more important than treatment. It is the best way to keep healthy. Therefore, health intervention is the key to prevent chronic diseases. Especially now, with the spread of COVID-19 pandemic, reducing the times of hospital check-ups and treatments for chronic patients is practically significant for releasing the stress on medical staffs and decreasing the rate of transmission and infection of COVID-19. In this paper, case-based reasoning (CBR) technology is used to assist personalized intervention for chronic diseases, and the key technologies of personalized intervention for chronic diseases based on case-based reasoning are proposed. The case organization, case retrieval, and case retention techniques of CBR technology in chronic disease personalized intervention are designed, and the calculation of interclass dispersion is added to the distribution of feature words, which is used to describe the distribution of feature attributes in different categories of cases. It provides an effective method for the establishment of personalized intervention model for chronic disease.


Subject(s)
Algorithms , Chronic Disease/prevention & control , Precision Medicine , COVID-19/epidemiology , COVID-19/prevention & control , COVID-19/transmission , China/epidemiology , Computational Biology , Humans , Mathematical Concepts , Models, Biological , Pandemics/prevention & control , Problem Solving , SARS-CoV-2
17.
Comput Math Methods Med ; 2021: 5556433, 2021.
Article in English | MEDLINE | ID: covidwho-1356984

ABSTRACT

The prediction of the dynamics of the COVID-19 outbreak and the corresponding needs of the health care system (COVID-19 patients' admissions, the number of critically ill patients, need for intensive care units, etc.) is based on the combination of a limited growth model (Verhulst model) and a short-term predictive model that allows predictions to be made for the following day. In both cases, the uncertainty analysis of the prediction is performed, i.e., the set of equivalent models that adjust the historical data with the same accuracy. This set of models provides the posterior distribution of the parameters of the predictive model that adjusts the historical series. It can be extrapolated to the same analyzed time series (e.g., the number of infected individuals per day) or to another time series of interest to which it is correlated and used, e.g., to predict the number of patients admitted to urgent care units, the number of critically ill patients, or the total number of admissions, which are directly related to health needs. These models can be regionalized, that is, the predictions can be made at the local level if data are disaggregated. We show that the Verhulst and the Gompertz models provide similar results and can be also used to monitor and predict new outbreaks. However, the Verhulst model seems to be easier to interpret and to use.


Subject(s)
COVID-19/epidemiology , Models, Biological , Pandemics , SARS-CoV-2 , COVID-19/transmission , Computational Biology , Health Services Needs and Demand , Humans , Mathematical Concepts , Models, Statistical , Pandemics/statistics & numerical data , Spain/epidemiology , Time Factors
18.
Rev Sci Instrum ; 92(7): 074101, 2021 Jul 01.
Article in English | MEDLINE | ID: covidwho-1338585

ABSTRACT

A fluid mechanics model of inhaled air gases, nitrogen (N2) and oxygen (O2) gases, and exhaled gas components (CO2 and water vapor particles) through a facial mask (membrane) to shield the COVID-19 virus is established. The model was developed based on several gas flux contributions that normally take place through membranes. Semiempirical solutions of the mathematical model were predicted for the N95 facial mask accounting on several parameters, such as a range of porosity size (i.e., 1-30 nm), void fraction (i.e., 10-3%-0.3%), and thickness of the membrane (i.e., 10-40 µm) in comparison to the size of the COVID-19 virus. A unitless number (Nr) was introduced for the first time to describe semiempirical solutions of O2, N2, and CO2 gases through the porous membrane. An optimum Nr of expressing the flow of the inhaled air gases, O2 and N2, through the porous membrane was determined (NO2 = NN2 = -4.4) when an N95 facial mask of specifications of a = 20 nm, l = 30 µm, and ε = 30% was used as a personal protection equipment (PPE). The concept of the optimum number Nr can be standardized not only for testing commercially available facial masks as PPEs but also for designing new masks for protecting humans from the COVID-19 virus.


Subject(s)
COVID-19/prevention & control , Masks , SARS-CoV-2 , Biomechanical Phenomena , Carbon Dioxide , Equipment Design , Exhalation , Gases , Humans , Hydrodynamics , Inhalation , Mathematical Concepts , Membranes, Artificial , Models, Theoretical , N95 Respirators , Nitrogen , Oxygen , Personal Protective Equipment , Porosity , Steam
19.
PLoS Comput Biol ; 17(7): e1009149, 2021 07.
Article in English | MEDLINE | ID: covidwho-1325366

ABSTRACT

The COVID-19 pandemic has created an urgent need for models that can project epidemic trends, explore intervention scenarios, and estimate resource needs. Here we describe the methodology of Covasim (COVID-19 Agent-based Simulator), an open-source model developed to help address these questions. Covasim includes country-specific demographic information on age structure and population size; realistic transmission networks in different social layers, including households, schools, workplaces, long-term care facilities, and communities; age-specific disease outcomes; and intrahost viral dynamics, including viral-load-based transmissibility. Covasim also supports an extensive set of interventions, including non-pharmaceutical interventions, such as physical distancing and protective equipment; pharmaceutical interventions, including vaccination; and testing interventions, such as symptomatic and asymptomatic testing, isolation, contact tracing, and quarantine. These interventions can incorporate the effects of delays, loss-to-follow-up, micro-targeting, and other factors. Implemented in pure Python, Covasim has been designed with equal emphasis on performance, ease of use, and flexibility: realistic and highly customized scenarios can be run on a standard laptop in under a minute. In collaboration with local health agencies and policymakers, Covasim has already been applied to examine epidemic dynamics and inform policy decisions in more than a dozen countries in Africa, Asia-Pacific, Europe, and North America.


Subject(s)
COVID-19 , Models, Biological , SARS-CoV-2 , Systems Analysis , Basic Reproduction Number , COVID-19/etiology , COVID-19/prevention & control , COVID-19/transmission , COVID-19 Testing , COVID-19 Vaccines , Computational Biology , Computer Simulation , Contact Tracing , Disease Progression , Hand Disinfection , Host Microbial Interactions , Humans , Masks , Mathematical Concepts , Pandemics , Physical Distancing , Quarantine , Software
20.
Bull Math Biol ; 83(8): 89, 2021 07 03.
Article in English | MEDLINE | ID: covidwho-1293427

ABSTRACT

This work presents a model-agnostic evaluation of four different models that estimate a disease's basic reproduction number. The evaluation presented is twofold: first, the theory behind each of the models is reviewed and compared; then, each model is tested with eight impartial simulations. All scenarios were constructed in an experimental framework that allows each model to fulfill its assumptions and hence, obtain unbiased results for each case. Among these models is the one proposed by Thompson et al. (Epidemics 29:100356, 2019), i.e., a Bayesian estimation method well established in epidemiological practice. The other three models include a novel state-space method and two simulation-based approaches based on a Poisson infection process. The advantages and flaws of each model are discussed from both theoretical and practical standpoints. Finally, we present the evolution of Covid-19 outbreak in Colombia as a case study for computing the basic reproduction number with each one of the reviewed methods.


Subject(s)
Basic Reproduction Number/statistics & numerical data , COVID-19/epidemiology , COVID-19/transmission , Pandemics/statistics & numerical data , SARS-CoV-2 , Bayes Theorem , Colombia/epidemiology , Computer Simulation , Confidence Intervals , Epidemics/statistics & numerical data , Humans , Mathematical Concepts , Models, Biological , Models, Statistical , Poisson Distribution
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