A mathematical model of COVID-19 transmission between frontliners and the general public

ABSTRACTThe number of COVID-19 cases is continuously increasing in different countries (as of March 2020) including the Philippines. It is estimated that the basic reproductive number of COVID-19 is around 1.5 to 4. The basic reproductive number characterizes the average number of persons that a primary case can directly infect in a population full of susceptible individuals. However, there can be superspreaders that can infect more than this estimated basic reproductive number. In this study, we formulate a conceptual mathematical model on the transmission dynamics of COVID-19 between the frontliners and the general public. We assume that the general public has a reproductive number between 1.5 to 4, and frontliners (e.g. healthcare workers, customer service and retail personnel, food service crews, and transport or delivery workers) have a higher reproduction number. Our simulations show that both the frontliners and the general public should be protected or resilient against the disease. Protecting only the frontliners will not result in flattening the epidemic curve. Protecting only the general public may flatten the epidemic curve but the infection risk faced by the frontliners is still high, which may eventually affect their work. Our simple model does not consider all factors involved in COVID-19 transmission in a community, but the insights from our model results remind us of the importance of community effort in controlling the transmission of the disease. All in all, the take-home message is that everyone in the community, whether a frontliner or not, should be protected or should implement preventive measures to avoid being infected.

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A MATHEMATICAL MODEL FOR HUMAN AND ANIMAL LEPTOSPIROSIS

Journal of Biological System ◽

10.1142/s0218339015400057 ◽

2015 ◽

Vol 23 (supp01) ◽

pp. S55-S65 ◽

Cited By ~ 4

Author(s):

DAVID BACA-CARRASCO ◽

DANIEL OLMOS ◽

IGNACIO BARRADAS

Keyword(s):

Mathematical Model ◽

Original Model ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Si Model

In this paper, we propose a SI model for the study of human and animal leptospirosis. Unlike other models for leptospirosis which consider only rodents as infection vectors, we consider that humans can be infected not only through contact with rodents, but also through any other animal that serves as a reservoir for the bacteria, and through contact with bacteria that are free in the environment. We calculate the basic reproductive number for this model, which is given in terms of the basic reproductive numbers of simpler subsystems of the original model, and propose some intervention techniques for controlling the disease based on our results.

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Effectiveness of control measures during the SARS epidemic in Beijing: a comparison of the Rt curve and the epidemic curve

Epidemiology and Infection ◽

10.1017/s0950268807008722 ◽

2007 ◽

Vol 136 (4) ◽

pp. 562-566 ◽

Cited By ~ 29

Author(s):

B. J. COWLING ◽

L. M. HO ◽

G. M. LEUNG

Keyword(s):

Public Health ◽

Quantitative Assessment ◽

Control Measures ◽

Transmission Dynamics ◽

Reproductive Number ◽

Primary Case ◽

Epidemic Curve ◽

Health Control

SUMMARYOne of the areas most affected by SARS was Beijing with 2521 reported cases. We estimate the effective reproductive number Rt for the Beijing SARS epidemic, which represents the average number of secondary cases per primary case on each day of the epidemic and is therefore a measure of the underlying transmission dynamics. Our results provide a quantitative assessment of the effectiveness of public health control measures. More generally, our results illustrate how changes in Rt will reflect changes in the epidemic curve.

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Epidemic Dynamics and Patterns of Plant Diseases

Phytopathology ◽

10.1094/phyto.2001.91.10.1001 ◽

2001 ◽

Vol 91 (10) ◽

pp. 1001-1010 ◽

Cited By ~ 68

Author(s):

J. Segarra ◽

M. J. Jeger ◽

F. van den Bosch

Keyword(s):

Plant Diseases ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Disease Rate ◽

Epidemic Threshold ◽

Differential Delay Equation ◽

Differential Delay ◽

Epidemic Curve ◽

Epidemic Dynamics ◽

Special Cases

The general Kermack and McKendrick epidemic model (K&M) is derived with an appropriate terminology for plant diseases. The epidemic dynamics and patterns of special cases of the K&M model, such as the Vanderplank differential-delay equation; the compartmental healthy (H), latent (L), infectious (S), and postinfectious (R) model; and the K&M model with a delay-gamma-distributed sporulation curve were compared. The characteristics of the disease cycle are summarized by the basic reproductive number, R0, and the normalized sporulation curve, i(τ). We show how R0 and the normalized sporulation curve can be calculated from data in the literature. There are equivalences in the values of the basic reproductive number, R0, the epidemic threshold, and the final disease level across the different models.However, they differ in expressions for the initial disease rate, r, and the initial infection, Q, because the values depend on the sporulation curve. Expressions for r and Q were obtained for each model and can be used to approximate the epidemic curve by the logistic equation.

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Sensitivity and mathematical model analysis on secondhand smoking tobacco

Journal of the Egyptian Mathematical Society ◽

10.1186/s42787-020-00108-1 ◽

2020 ◽

Vol 28 (1) ◽

Author(s):

Birliew Fekede ◽

Benyam Mebrate

Keyword(s):

Mathematical Model ◽

Equilibrium Point ◽

Equilibrium Points ◽

Reproductive Number ◽

Primary Case ◽

Susceptible Population ◽

Proposed Model ◽

Relative Change ◽

Well Posed ◽

Mathematical Model Analysis

AbstractIn this paper, we are concerned with a mathematical model of secondhand smoker. The model is biologically meaningful and mathematically well posed. The reproductive number $$R_{0}$$ R 0 is determined from the model, and it measures the average number of secondary cases generated by a single primary case in a fully susceptible population. If $$R_{0}<1,$$ R 0 < 1 , the smoking-free equilibrium point is stable, and if $$R_{0}>1,$$ R 0 > 1 , endemic equilibrium point is unstable. We also provide numerical simulation to show stability of equilibrium points. In addition, sensitivity analysis of parameters involving in the dynamic system of the proposed model has been included. The parameters involving in reproductive number measure the relative change in $$R_{0}$$ R 0 when the value of the parameter changes.

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Bayesian approach for modelling the dynamic of COVID-19 outbreak on the Diamond Princess Cruise Ship

10.1101/2020.06.21.20136465 ◽

2020 ◽

Author(s):

Chao-Chih Lai ◽

Chen-Yang Hsu ◽

Hsiao-Hsuan Jen ◽

Amy Ming-Fang Yen ◽

Chang-Chuan Chan ◽

...

Keyword(s):

Population Size ◽

Large Population ◽

Credible Interval ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Cruise Ship ◽

Epidemic Curve ◽

Cruise Ships ◽

Epidemic Period ◽

Containment Measures

AbstractThe outbreaks of acute respiratory infectious disease with high attack rates on cruise ships were rarely studied. The outbreak of COVID-19 on the Diamond Princess Cruise Ship provides an unprecedented opportunity to estimate its original transmissibility with basic reproductive number (R0) and the effectiveness of containment measures. The traditional deterministic approach for estimating R0 is based on the outbreak of a large population size rather than that a small cohort of cruise ship. The parameters are therefore fraught with uncertainty. To tackle this problem, we developed a Bayesian Susceptible-Exposed-Infected-Recovery (SEIR) model with ordinary differential equation (ODE) to estimate three parameters, including transmission coefficients, the latent period, and the recovery rate given the uncertainty implicated the outbreak of COVID-19 on cruise ship with modest population size. Based on the estimated results on these three parameters before the introduction of partial containment measures, the natural epidemic curve after intervention was predicted and compared with the observed curve in order to assess the efficacy of containment measures. With the application of the Bayesian model to the empirical data on COVID-19 outbreak on the Diamond Princess Cruise Ship, the R0 was estimated as high as 5.71(95% credible interval: 4.08-7.55) because of its aerosols and fomite transmission mode. The simulated trajectory shows the entire epidemic period without containment measurements was approximately 47 days and reached the peak one month later after the index case. The partial containment measure reduced 34% (95% credible interval: 31-36%) infected passengers. Such a discovery provides an insight into timely evacuation and early isolation and quarantine with decontamination for containing other cruise ships and warship outbreaks.

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Application of a Mathematical Model in Determining the Spread of the Rabies Virus: Simulation Study

JMIR Medical Informatics ◽

10.2196/18627 ◽

2020 ◽

Vol 8 (5) ◽

pp. e18627

Author(s):

Yihao Huang ◽

Mingtao Li

Keyword(s):

Mathematical Model ◽

Rabies Virus ◽

Control Measures ◽

Transmission Mode ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Stable Range ◽

Rabies Control ◽

Number Of Patients ◽

Acute Infectious Disease

Background Rabies is an acute infectious disease of the central nervous system caused by the rabies virus. The mortality rate of rabies is almost 100%. For some countries with poor sanitation, the spread of rabies among dogs is very serious. Objective The objective of this paper was to study the ecological transmission mode of rabies to make theoretical contributions to the suppression of rabies in China. Methods A mathematical model of the transmission mode of rabies was constructed using relevant data from the literature and officially published figures in China. Using this model, we fitted the data of the number of patients with rabies and predicted the future number of patients with rabies. In addition, we studied the effectiveness of different rabies suppression measures. Results The results of the study indicated that the number of people infected with rabies will rise in the first stage, and then decrease. The model forecasted that in about 10 years, the number of rabies cases will be controlled within a relatively stable range. According to the prediction results of the model reported in this paper, the number of rabies cases will eventually plateau at approximately 500 people every year. Relatively effective rabies suppression measures include controlling the birth rate of domestic and wild dogs as well as increasing the level of rabies immunity in domestic dogs. Conclusions The basic reproductive number of rabies in China is still greater than 1. That is, China currently has insufficient measures to control rabies. The research on the transmission mode of rabies and control measures in this paper can provide theoretical support for rabies control in China.

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Reconciling early-outbreak estimates of the basic reproductive number and its uncertainty: framework and applications to the novel coronavirus (SARS-CoV-2) outbreak

10.1101/2020.01.30.20019877 ◽

2020 ◽

Cited By ~ 21

Author(s):

Sang Woo Park ◽

Benjamin M. Bolker ◽

David Champredon ◽

David J. D. Earn ◽

Michael Li ◽

...

Keyword(s):

Basic Reproductive Number ◽

Reproductive Number ◽

Similar Data ◽

Primary Case ◽

Susceptible Population ◽

Generation Interval ◽

Statistical Framework ◽

Wide Range ◽

Novel Coronavirus ◽

Global Threat

AbstractA novel coronavirus (SARS-CoV-2) has recently emerged as a global threat. As the epidemic progresses, many disease modelers have focused on estimating the basic reproductive number ℛ0– the average number of secondary cases caused by a primary case in an otherwise susceptible population. The modeling approaches and resulting estimates of ℛ0 vary widely, despite relying on similar data sources. Here, we present a novel statistical framework for comparing and combining different estimates of ℛ0 across a wide range of models by decomposing the basic reproductive number into three key quantities: the exponential growth rate r, the mean generation interval , and the generation-interval dispersion κ. We then apply our framework to early estimates of ℛ0 for the SARS-CoV-2 outbreak. We show that many early ℛ0 estimates are overly confident. Our results emphasize the importance of propagating uncertainties in all components of ℛ0, including the shape of the generation-interval distribution, in efforts to estimate ℛ0 at the outset of an epidemic.

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A Mathematical Analysis of an In-vivo Ebola Virus Transmission Dynamics Model

Tanzania Journal of Science ◽

10.4314/tjs.v47i4.12 ◽

2021 ◽

Vol 47 (4) ◽

pp. 1464-1477

Author(s):

Seleman Ismail ◽

Adeline Peter Mtunya

Keyword(s):

Mathematical Model ◽

Infection Rate ◽

Ebola Virus ◽

Virus Transmission ◽

Transmission Dynamics ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Model Parameters ◽

Sensitivity Index

Ebola virus (EBOV) infection is a hemorrhagic and hazardous disease, which is among the most shocking threats to human health causing a large number of deaths. Currently, there are no approved curative therapies for the disease. In this study, a mathematical model for in-vivo Ebola virus transmission dynamics was analyzed. The analysis of the model mainly focused on the sensitivity of basic reproductive number, pertaining to the model parameters. Particularly, the sensitivity indices of all parameters of were computed by using the forward normalized sensitivity index method. The results showed that a slight change in the infection rate immensely influences while the same change in the production rate of the virus has the least impact on . Thus, , being a determining factor of the disease progression, deliberate control measures targeting the infection rate, the most positively sensitive parameter, are required. This implies that reducing infection rate will redirect the disease to extinction. Keywords: Ebola virus infection, immune response, sensitivity index, mathematical model.

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Mathematical Modelling of the Addiction of Drug Substances among Students in Tertiary Institutions in Nigeria

Journal of Biomedical Research & Environmental Sciences ◽

10.37871/jbres1322 ◽

2021 ◽

Vol 2 (9) ◽

pp. 851-856

Author(s):

Adeyemi O Binuyo ◽

Oludare Temitope Osuntokun

Keyword(s):

Mathematical Model ◽

Drug Addiction ◽

Drug Users ◽

Recruitment Rate ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Tertiary Institutions ◽

Drug Substances ◽

The Mathematical Model ◽

Drug Free

In this paper, we formulated a mathematical model for the addiction of drug substances among students in the tertiary institutions in Nigeria. The model explains the dynamics of the use and the addiction of certain substances that are perceived as mood changing by the students in the tertiary institutions in Nigeria. The drug model will be analysed qualitatively. The basic reproductive number which is the drug addiction number of the mathematical model was determined using the next generation procedure. It was found that the drug free equilibrium point was found to be locally asymptotically stable whenever the drug addiction number is less than one and unstable otherwise. The analysis revealed that an increase in the recruitment rate of students and the rate at which the students return to the use and addiction of drugs would cause an increase in the drug addiction number. There are impacts on interaction among non-drug users and drug users in the system with time. An increase in the contact or limitation rate increases the population of drug users. It is hereby recommended that; government should intensify efforts to reduce or stop the spread of selling and purchasing of the drug substances through government policies among the students in the tertiary institutions in Nigeria.

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Boundedness and Stability Properties of Solutions of Mathematical Model of Measles.

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.52.2021.3367 ◽

2021 ◽

Vol 52 (1) ◽

pp. 91-112

Author(s):

Babatunde Sunday Ogundare ◽

James Akingbade

Keyword(s):

Mathematical Model ◽

Asymptotic Stability ◽

Global Asymptotic Stability ◽

Endemic Equilibrium ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Jacobian Determinant ◽

Stability Of Solutions ◽

Open Population ◽

Disease Free

In this paper, asymptotic stability and global asymptotic stability of solutions to a deterministic and compartmental mathematical model of measles infection is considered using the ideas of the Jacobian determinant as well as the second method of Lyapunov, criteria/conditions that guaranteed asymptotic stability of disease free equilibrium and endemic equilibrium were established. Also the basic reproductive number $R_0$ was obtained. The results in this work compliments existing work and provided further information in controlling the disease in an open population.

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