scholarly journals A model for COVID-19 with isolation, quarantine and testing as control measures

2020 ◽  
Author(s):  
M.S. Aronna ◽  
R. Guglielmi ◽  
L.M. Moschen
Keyword(s):  
Compartmental Model ◽  
Reproduction Number ◽  
Risk Groups ◽  
Control Measures ◽  
Contact Rate ◽  
Control Parameters ◽  
Social Distancing ◽  
Proposed Model ◽  
Asymptomatic Infections ◽  
The Basic Reproduction Number

AbstractIn this article we propose a compartmental model for the dynamics of Coronavirus Disease 2019 (COVID-19). We take into account the presence of asymptomatic infections and the main policies that have been adopted so far to contain the epidemic: isolation (or social distancing) of a portion of the population, quarantine for confirmed cases and testing. We model isolation by separating the population in two groups: one composed by key-workers that keep working during the pandemic and have a usual contact rate, and a second group consisting of people that are enforced/recommended to stay at home. We refer to quarantine as strict isolation, and it is applied to confirmed infected cases.In the proposed model, the proportion of people in isolation, the level of contact reduction and the testing rate are control parameters that can vary in time, representing policies that evolve in different stages. We obtain an explicit expression for the basic reproduction number in terms of the parameters of the disease and of the control policies. In this way we can quantify the effect that isolation and testing have in the evolution of the epidemic. We present a series of simulations to illustrate different realistic scenarios. From the expression of and the simulations we conclude that isolation (social distancing) and testing among asymptomatic cases are fundamental actions to control the epidemic, and the stricter these measures are and the sooner they are implemented, the more lives can be saved. Additionally, we show that people that remain in isolation significantly reduce their probability of contagion, so risk groups should be recommended to maintain a low contact rate during the course of the epidemic.

scholarly journals Global stability analysis and control of leptospirosis

2016 ◽  
Vol 14 (1) ◽  
pp. 567-585 ◽  
Author(s):  
Kazeem Oare Okosun ◽  
M. Mukamuri ◽  
Daniel Oluwole Makinde
Keyword(s):  
Cost Effectiveness ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Cost Effective ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Control Parameters ◽  
Constant Control ◽  
Preventive Vaccination ◽  
The Basic Reproduction Number

AbstractThe aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.

scholarly journals Role of Mathematical Model in Curbing COVID-19 in Nigeria

2021 ◽  
Vol 3 (2) ◽  
pp. 135-147
Author(s):  
Chinwendu Emilian Madubueze ◽  
Nkiru Maria Akabuike ◽  
Sambo Dachollom
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Viral Disease ◽  
Control Measures ◽  
Social Distancing ◽  
Testing Rate ◽  
Intervention Measures ◽  
The Impact ◽  
The Basic Reproduction Number

COVID-19 is a viral disease that is caused by Severe Acute Respiratory Syndrome coronavirus 2 (SARSCoV-2) which has no approved vaccine. Based on the available non-pharmacological interventions like wearing of face masks, observing social distancing, and lockdown, this work assesses the impact of non-pharmaceutical control measures (social distancing and use of face-masks) and mass testing on the transmission of COVID-19 in Nigeria. A mathematical model for COVID-19 is formulated with intervention measures (observing social distancing and wearing of face masks) and mass testing. The basic reproduction number, R_0, is computed using next-generation method while the disease-free equilibrium is found to be locally and globally asymptotically stable when R_0< 1. The model is parameterized using Nigeria data on COVID-19 in Nigeria. The basic reproduction number is found to be less than unity (R_0 < 1) either when the compliance with intervention measures is moderate (50% <= alpha< 70%) and the testing rate per day is moderate (0,5 <=alpha_2 < 0,7) or when the compliance with intervention measures is strict (alpha>=70%) and the testing rate per day is poor (alpha_2 = 0,3). This implies that Nigeria will be able to halt the spread of COVID-19 under these two conditions. However, it will be easier to enforce strict compliance with intervention measures in the presence of poor testing rate due to the limited availability of testing facilities and manpower in Nigeria. Hence, this study advocates that Nigerian governments (Federal and States) should aim at achieving a testing rate of at least 0.3 per day while ensuring that all the citizens strictly comply with wearing face masks and observing social distancing in public.

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 Impact of early detection and vaccination strategy in COVID-19 eradication program in Jakarta, Indonesia

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Dipo Aldila ◽  
Brenda M. Samiadji ◽  
Gracia M. Simorangkir ◽  
Sarbaz H. A. Khosnaw ◽  
Muhammad Shahzad
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vaccination Strategy ◽  
Vaccination Rate ◽  
Rapid Testing ◽  
Social Distancing ◽  
Rapid Spread ◽  
Vaccine Potential ◽  
The Basic Reproduction Number

Abstract Objective Several essential factors have played a crucial role in the spreading mechanism of COVID-19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several non-pharmaceutical interventions. Because of the rapid spread of COVID-19 worldwide, understanding the significance of these factors is crucial in determining whether COVID-19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID-19 considering mentioned factors. Results Infection detection and vaccination have the potential to eradicate COVID-19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID-19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID-19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID-19 vaccine potential.

Mathematical Modeling and Analysis of Covid-19 Infection spreads in India with Restricted Optimal Treatment on Disease Incidence

BIOMATH ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2106147
Author(s):  
Debkumar Pal ◽  
D Ghosh ◽  
P K Santra ◽  
G S Mahapatra
Keyword(s):  
Mathematical Modeling ◽  
Objective Function ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Treatment Control ◽  
Modeling And Analysis ◽  
Proposed Model ◽  
The Cost ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

scholarly journals APLIKASI MODEL EPIDEMIK SEIAR-SEI PADA PENYEBARAN PENYAKIT MALARIA DENGAN INFEKSI ASIMTOMATIK DAN SUPER INFEKSI

2018 ◽  
Vol 15 (2) ◽  
pp. 67
Author(s):  
Stella Maryana Belwawin
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Asymptomatic Infection ◽  
Endemic Equilibrium ◽  
Asymptomatic Infections ◽  
The Stability ◽  
Super Infection ◽  
The Basic Reproduction Number

AbstractThis aim of this study is to determine the point of equilibrium and analyze the stability of SEIAR-SEI model on malaria disease with asymptomatic infection, super infection and the effect of the mosquito's life cycle. This study also aim is to measure the sensitivity of the spread of malaria to the parameters of asymptomatic infections, the rate of treatment, and the rate of birth of mosquitoes through the magnitude of . The method in this research is deductively, through several stage, such as  determination of disease-free equilibrium point and endemic equilibrium point, determination of basic reproduction number (), analyze of the basic reproduction number sensitivity of the spread of malaria to the parameters of asymptomatic infections, the rate of treatment, and the rate of birth of mosquitoes. The endemic equilibrium point was obtained using rule of Descartes. The result show that the change in the value of parameter , , and  has effect on the basic reproduction number (). Treatment factors in the human population influence the elimination of malaria in a population. Whereas asymptomatic infection factors and the birth rate of adult mosquitoes influence the increase in malaria infection. Keywords:  Malaria, asymptomatic infection, super infection, basic reproduction number, rule of descrates. AbstrakPenelitian ini bertujuan menentukan titik keseimbangan dan menganalisis kestabilan dari model SEIAR_SEI pada penyakit malaria dengan pengaruh infeksi asimtomatik, super infeksi, dan siklus hidup nyamuk. Penelitian ini juga bertujuan mengukur tingkat sensitivitas penyebaran penyakit malaria terhadap parameter infeksi asimtomatik, laju pengobatan, serta laju kelahiran nyamuk.melalu besaran .  Metode yang digunakan dalam penelitian ini adalah metode deduktif dengan langkah-langkah : menentukan titik keseimbangan bebas penyakit dan endemik dan menentukan bilangan reproduksi dasar ). Analisis sensitivitas bilangan reproduksi dasar dilakukan terhadap parameter infeksi asimtomatik, pengobatan, dan laju kelahiran nyamuk. Tititk keseimbangan endemik diperoleh dengan aturan descrates. Hasil yang diperoleh menunjukkan parameter , , dan  berpengaruh terhadap bilangan reproduksi dasar (). Faktor pengobatan berpengaruh terhadap eliminasi penyakit malaria. Sedangkan faktor infeksi asimtomatik dan laju kelahiran nyamuk dewasa berpengaruh terhadap peningkatan infeksi penyakit malaria. Kata kunci: Malaria, Infeksi Asimtomatik, Super Infeksi, Bilangan Reproduksi Dasar, Aturan Descrates . 

scholarly journals Estimates of the ongoing need for social distancing and control measures post-“lockdown” from trajectories of COVID-19 cases and mortality

2020 ◽  
Vol 56 (1) ◽  
pp. 2001483 ◽  
Author(s):  
Mike Lonergan ◽  
James D. Chalmers
Keyword(s):  
Severe Acute Respiratory Syndrome ◽  
Economic Activity ◽  
Regression Models ◽  
Reproduction Number ◽  
Viral Transmission ◽  
Control Measures ◽  
Social Distancing ◽  
And Control ◽  
Doubling Times

By 21 May 2020, severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) had caused more than 5 million cases of coronavirus 2019 (COVID-19) across more than 200 countries. Most countries with significant outbreaks have introduced social distancing or “lockdown” measures to reduce viral transmission. So the key question now is when, how and to what extent these measures can be lifted.Publicly available data on daily numbers of newly confirmed cases and mortality were used to fit regression models estimating trajectories, doubling times and the reproduction number (R0) of the disease, before and under the control measures. These data ran up to 21 May 2020, and were sufficient for analysis in 89 countries.The estimates of R0 before lockdown based on these data were broadly consistent with those previously published: between 2.0 and 3.7 in the countries with the largest number of cases available for analysis (USA, Italy, Spain, France and UK). There was little evidence to suggest that the restrictions had reduced R far below 1 in many places, with France having the most rapid reductions: R0 0.76 (95% CI 0.72–0.82) based on cases, and 0.77 (95% CI 0.73–0.80) based on mortality.Intermittent lockdown has been proposed as a means of controlling the outbreak while allowing periods of increased freedom and economic activity. These data suggest that few countries could have even 1 week per month unrestricted without seeing resurgence of the epidemic. Similarly, restoring 20% of the activity that has been prevented by the lockdowns looks difficult to reconcile with preventing the resurgence of the disease in most countries.

scholarly journals Prediction of confinement effects on the number of Covid-19 outbreak in Algeria

2020 ◽  
Vol 15 ◽  
pp. 37 ◽  
Author(s):  
Ali Moussaoui ◽  
Pierre Auger
Keyword(s):  
Reproduction Number ◽  
Control Measures ◽  
Cumulative Number ◽  
Time Data ◽  
Final Size ◽  
First Case ◽  
Algerian Population ◽  
Fast Change ◽  
Real Time Data ◽  
The Basic Reproduction Number

The first case of coronavirus disease 2019 (COVID-19) in Algeria was reported on 25 February 2020. Since then, it has progressed rapidly and the number of cases grow exponentially each day. In this article, we utilize SEIR modelling to forecast COVID-19 outbreak in Algeria under two scenarios by using the real-time data from March 01 to April 10, 2020. In the first scenario: no control measures are put into place, we estimate that the basic reproduction number for the epidemic in Algeria is 2.1, the number of new cases in Algeria will peak from around late May to early June and up to 82% of the Algerian population will likely contract the coronavirus. In the second scenario, at a certain date T, drastic control measures are taken, people are being advised to self-isolate or to quarantine and will be able to leave their homes only if necessary. We use SEIR model with fast change between fully protected and risky states. We prove that the final size of the epidemic depends strongly on the cumulative number of cases at the date when we implement intervention and on the fraction of the population in confinement. Our analysis shows that the longer we wait, the worse the situation will be and this very quickly produces.

scholarly journals Estimating the critical immunity threshold for preventing hepatitis A outbreaks in men who have sex with men

2015 ◽  
Vol 144 (7) ◽  
pp. 1528-1537 ◽  
Author(s):  
D. G. REGAN ◽  
J. G. WOOD ◽  
C. BENEVENT ◽  
H. ALI ◽  
L. WATCHIRS SMITH ◽  
...  
Keyword(s):  
High Risk ◽  
Hepatitis A ◽  
Hepatitis A Virus ◽  
Reproduction Number ◽  
Vaccine Coverage ◽  
Risk Groups ◽  
Developed Countries ◽  
Population Immunity ◽  
Sex With Men ◽  
The Basic Reproduction Number

SUMMARYSeveral outbreaks of hepatitis A in men who have sex with men (MSM) were reported in the 1980s and 1990s in Australia and other countries. An effective hepatitis A virus (HAV) vaccine has been available in Australia since 1994 and is recommended for high-risk groups including MSM. No outbreaks of hepatitis A in Australian MSM have been reported since 1996. In this study, we aimed to estimate HAV transmissibility in MSM populations in order to inform targets for vaccine coverage in such populations. We used mathematical models of HAV transmission in a MSM population to estimate the basic reproduction number (R0) and the probability of an HAV epidemic occurring as a function of the immune proportion. We estimated a plausible range forR0of 1·71–3·67 for HAV in MSM and that sustained epidemics cannot occur once the proportion immune to HAV is greater than ~70%. To our knowledge this is the first estimate ofR0and the critical population immunity threshold for HAV transmission in MSM. As HAV is no longer endemic in Australia or in most other developed countries, vaccination is the only means of maintaining population immunity >70%. Our findings provide impetus to promote HAV vaccination in high-risk groups such as MSM.

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.

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