scholarly journals Effect of density dependence on coinfection dynamics

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Jonathan Andersson ◽  
Samia Ghersheen ◽  
Vladimir Kozlov ◽  
Vladimir G. Tkachev ◽  
Uno Wennergren
Keyword(s):  
Carrying Capacity ◽  
Compartmental Model ◽  
Stable Equilibrium ◽  
Reproduction Number ◽  
Point Of View ◽  
Volterra Model ◽  
Vital Rates ◽  
Fundamental Parameters ◽  
Infection Dynamics ◽  
Progression Of Disease

AbstractIn this paper we develop a compartmental model of SIR type (the abbreviation refers to the number of Susceptible, Infected and Recovered people) that models the population dynamics of two diseases that can coinfect. We discuss how the underlying dynamics depends on the carrying capacity K: from a simple dynamics to a more complex. This can also help in understanding the appearance of more complicated dynamics, for example, chaos and periodic oscillations, for large values of K. It is also presented that pathogens can invade in population and their invasion depends on the carrying capacity K which shows that the progression of disease in population depends on carrying capacity. More specifically, we establish all possible scenarios (the so-called transition diagrams) describing an evolution of an (always unique) locally stable equilibrium state (with only non-negative compartments) for fixed fundamental parameters (density independent transmission and vital rates) as a function of the carrying capacity K. An important implication of our results is the following important observation. Note that one can regard the value of K as the natural ‘size’ (the capacity) of a habitat. From this point of view, an isolation of individuals (the strategy which showed its efficiency for COVID-19 in various countries) into smaller resp. larger groups can be modelled by smaller resp. bigger values of K. Then we conclude that the infection dynamics becomes more complex for larger groups, as it fairly maybe expected for values of the reproduction number $$R_0\approx 1$$ R 0 ≈ 1 . We show even more, that for the values $$R_0>1$$ R 0 > 1 there are several (in fact four different) distinguished scenarios where the infection complexity (the number of nonzero infected classes) arises with growing K. Our approach is based on a bifurcation analysis which allows to generalize considerably the previous Lotka-Volterra model considered previously in Ghersheen et al. (Math Meth Appl Sci 42(8), 2019).

scholarly journals Modelling COVID-19 transmission in Africa: countrywise projections of total and severe infections under different lockdown scenarios

BMJ Open ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. e044149
Author(s):  
Isabel Frost ◽  
Jessica Craig ◽  
Gilbert Osena ◽  
Stephanie Hauck ◽  
Erta Kalanxhi ◽  
...  
Keyword(s):  
Vulnerable Populations ◽  
Compartmental Model ◽  
African Continent ◽  
Economic Costs ◽  
African Countries ◽  
Exponential Increase ◽  
Progression Of Disease ◽  
Severe Infections ◽  
Potential Impact ◽  
Hiv Aids

ObjectivesAs of 13 January 2021, there have been 3 113 963 confirmed cases of SARS-CoV-2 and 74 619 deaths across the African continent. Despite relatively lower numbers of cases initially, many African countries are now experiencing an exponential increase in case numbers. Estimates of the progression of disease and potential impact of different interventions are needed to inform policymaking decisions. Herein, we model the possible trajectory of SARS-CoV-2 in 52 African countries under different intervention scenarios.DesignWe developed a compartmental model of SARS-CoV-2 transmission to estimate the COVID-19 case burden for all African countries while considering four scenarios: no intervention, moderate lockdown, hard lockdown and hard lockdown with continued restrictions once lockdown is lifted. We further analysed the potential impact of COVID-19 on vulnerable populations affected by HIV/AIDS and tuberculosis (TB).ResultsIn the absence of an intervention, the most populous countries had the highest peaks in active projected number of infections with Nigeria having an estimated 645 081 severe infections. The scenario with a hard lockdown and continued post-lockdown interventions to reduce transmission was the most efficacious strategy for delaying the time to the peak and reducing the number of cases. In South Africa, projected peak severe infections increase from 162 977 to 2 03 261, when vulnerable populations with HIV/AIDS and TB are included in the analysis.ConclusionThe COVID-19 pandemic is rapidly spreading across the African continent. Estimates of the potential impact of interventions and burden of disease are essential for policymakers to make evidence-based decisions on the distribution of limited resources and to balance the economic costs of interventions with the potential for saving lives.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

scholarly journals A Stochastic TB Model for a Crowded Environment

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Sibaliwe Maku Vyambwera ◽  
Peter Witbooi
Keyword(s):  
Compartmental Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Equation Model ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
The Stability ◽  
Crowded Environments ◽  
Disease Free

We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease-free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability of the disease-free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.

Strengthening and widening of steel pony truss bridges

1977 ◽  
Vol 4 (2) ◽  
pp. 214-225
Author(s):  
Baidar Bakht ◽  
Paul F. Csagoly
Keyword(s):  
Traffic Safety ◽  
Carrying Capacity ◽  
Point Of View ◽  
Load Carrying Capacity ◽  
Truss Bridges ◽  
Load Carrying ◽  
Live Loads ◽  
Pros And Cons ◽  
Pony Truss Bridge ◽  
Truss Bridge

There are many thousands of existing pony truss bridges in North America which were constructed in the earlier part of this century and are still serving as important traffic carriers. The present economic situation demands that these bridges should usefully serve their purpose for as long as is safely possible.These bridges could be found inadequate for either or both of the following reasons. With the exception of remote areas, operational traffic safety would require two 12-ft lanes plus adequate shoulders. Many of these old bridges are therefore unsatisfactory from the geometrical point of view. Some bridges were designed for live loads that are only a fraction of present commercial vehicle weights.A computer-oriented method of rigorous analysis of lateral buckling behaviour of pony truss bridges is briefly discussed. The method is implemented through a computer program which has been validated by experimental data. It is expected that the program would predict realistic values of load-carrying capacity of such bridges and would help to avoid many an unnecessary replacement.Various methods of strengthening and widening pony truss bridges, and their pros and cons, are discussed. It is shown that the strengthening of a few components of a pony truss bridge does not always lead to an increase in the load-carrying capacity of the bridge.

scholarly journals Social Acceptance of Aquaculture in Spain: An Instrument to Achieve Sustainability for Society

2020 ◽  
Vol 17 (18) ◽  
pp. 6628
Author(s):  
José Ruiz-Chico ◽  
José M. Biedma-Ferrer ◽  
Antonio R. Peña-Sánchez ◽  
Mercedes Jiménez-García
Keyword(s):  
Carrying Capacity ◽  
Social Acceptance ◽  
Point Of View ◽  
Saturation Point ◽  
Traditional Fishing ◽  
Further Development

Aquaculture is a technique to produce food that is under debate, due to its possible consequences for altering the economy, traditional fishing included, or the environment, even with doubts about the health of consumers. This document studies its social acceptance from the point of view of carrying capacity. This term is defined as the level at which this activity begins to be disproportionate and poses important disadvantages for society. In this context, we conducted 803 surveys in six coastal provinces in Spain. The results show that the acceptance of these products is good, implying that aquaculture is far from reaching its saturation point in society. Additionally, the respondents gave a higher priority to socio-economic objectives than to environmental ones. We can conclude that the further development of this sector is advisable in these provinces. The general perception of aquaculture is better among men, and also among higher-income consumers. Informative activities should be organized to target these more hesitant groups. Production structures should be revised to overcome biases in the population about the idea that the food obtained from aquaculture harms the environment or is less natural or healthy. The possible abuse of feed and chemicals spreads this idea, and this could affect the taste and quality adversely.

The basic reproduction number

2012 ◽  
Author(s):  
Odo Diekmann ◽  
Hans Heesterbeek ◽  
Tom Britton
Keyword(s):  
Infectious Disease ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Infected Individual ◽  
Vital Role ◽  
Point Of View ◽  
Epidemiological Models ◽  
Disease Epidemiology ◽  
Infectious Disease Epidemiology ◽  
The Basic Reproduction Number

The basic reproduction number (or ratio) R₀ is arguably the most important quantity in infectious disease epidemiology. It is among the quantities most urgently estimated for infectious diseases in outbreak situations, and its value provides insight when designing control interventions for established infections. From a theoretical point of view R₀ plays a vital role in the analysis of, and consequent insight from, infectious disease models. There is hardly a paper on dynamic epidemiological models in the literature where R₀ does not play a role. R₀ is defined as the average number of new cases of an infection caused by one typical infected individual, in a population consisting of susceptibles only. This chapter shows how R₀ can be characterized mathematically and provides detailed examples of its calculation in terms of parameters of epidemiological models, culminating in a set of algorithms (or “recipes”) for the calculation for compartmental epidemic systems.

scholarly journals Prediction of the Peak, Effect of Intervention, and Total Infected by COVID-19 in India

2020 ◽  
pp. 1-11
Author(s):  
Parth Vipul Shah
Keyword(s):  
Health Care ◽  
Infection Rate ◽  
Compartmental Model ◽  
Total Population ◽  
Reproduction Number ◽  
Least Square Method ◽  
Peak Effect ◽  
Least Square ◽  
Intervention Period ◽  
Care Capacity

ABSTRACT Objectives: We study the effect of the coronavirus disease 2019 (COVID-19) in India and model the epidemic to guide those involved in formulating policy and building health-care capacity. Methods: This effect is studied using the Susceptible-Exposed-Infected-Recovered (SEIR) compartmental model. We estimate the infection rate using a least square method with Poisson noise and calculate the reproduction number. Results: The infection rate is estimated to be 0.270 and the reproduction number to be 2.70. The approximate peak of the epidemic will be August 9, 2020. A 25% drop in infection rate will delay the peak by 11 d for a 1-mo intervention period. The total infected individuals in India will be 9% of the total population. Conclusions: The predictions are sensitive to changes in the behavior of people and their practice of social distancing.

scholarly journals Is Nigeria really on top of COVID-19? Message from effective reproduction number

2020 ◽  
Author(s):  
Adeshina Israel Adekunle ◽  
Oyelola Adegboye ◽  
Ezra Gayawan ◽  
Emma McBryde
Keyword(s):  
Public Health ◽  
Compartmental Model ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Credible Interval ◽  
Control Measures ◽  
Maximum Value ◽  
Intervention Measures ◽  
Death Cases ◽  
Epidemiological Parameters

Following the importation of Covid-19 into Nigeria on the 27 February 2020 and then the outbreak, the question is: how do we anticipate the progression of the ongoing epidemics following all the intervention measures put in place? This kind of question is appropriate for public health responses and it will depend on the early estimates of the key epidemiological parameters of the virus in a defined population. In this study, we combined a likelihood-based method using a Bayesian framework and compartmental model of the epidemic of Covid-19 in Nigeria to estimate the effective reproduction number (R(t)) and basic reproduction number (R_0). This also enables us to estimate the daily transmission rate (β) that determines the effect of social distancing. We further estimate the reported fraction of symptomatic cases. The models are applied to the NCDC data on Covid-19 symptomatic and death cases from 27 February 2020 and 7 May 2020. In this period, the effective reproduction number is estimated with a minimum value of 0.18 and a maximum value of 1.78. Most importantly, the R(t) is strictly greater than one from April 13 till 7 May 2020. The R_0 is estimated to be 2.42 with credible interval: (2.37, 2.47). Comparing this with the R(t) shows that control measures are working but not effective enough to keep R(t) below one. Also, the estimated fractional reported symptomatic cases are between 10 to 50%. Our analysis has shown evidence that the existing control measures are not enough to end the epidemic and more stringent measures are needed.

scholarly journals A random forest model for forecasting regional COVID-19 cases utilizing reproduction number estimates and demographic data

2021 ◽  
Author(s):  
Joseph Galasso ◽  
Duy M. Cao ◽  
Robert Hochberg
Keyword(s):  
Random Forest ◽  
Human Error ◽  
Compartmental Model ◽  
Reproduction Number ◽  
Local Level ◽  
Demographic Data ◽  
Compartmental Models ◽  
Random Forest Model ◽  
Public Health Response ◽  
Forest Model

During the COVID-19 pandemic, predicting case spikes at the local level is important for a precise, targeted public health response and is generally done with compartmental models. The performance of compartmental models is highly dependent on the accuracy of their assumptions about disease dynamics within a population; thus, such models are susceptible to human error, unexpected events, or unknown characteristics of a novel infectious agent like COVID-19. We present a relatively non-parametric random forest model that forecasts the number of COVID-19 cases at the U.S. county level. Its most prioritized training features are derived from easily accessible, standard epidemiological data (i.e., regional test positivity rate) and the effective reproduction number R(t) from compartmental models. A novel input training feature is case projections generated by aligning estimated effective reproduction number from a compartmental model with real time testing data until maximally correlated, helping our model fit better to the epidemic's trajectory ascertained by traditional models. Any poor reliability of R(t) due to flaws in the compartmental model are mitigated with dynamic population mobility and prevalence and mortality of non-COVID-19 diseases to gauge population disease susceptibility. The model was used to generate forecasts for 1, 2, 3, and 4 weeks into the future for each reference week within 11/01/2020 - 01/10/2021 for 3068 counties. Over this time period, it maintained a mean absolute error (MAE) of less than 300 weekly cases/100,000 and consistently outperformed or performed comparably with gold-standard compartmental models. Furthermore, it holds great potential in ensemble modeling due to its potential for a more expansive training feature set while maintaining good performance and limited resource utilization.

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