MATHEMATICAL STUDY OF THE IMPACT OF QUARANTINE, ISOLATION AND VACCINATION IN CURTAILING AN EPIDEMIC

The quarantine of suspected cases and isolation of individuals with symptoms are two of the primary public health control measures for combating the spread of a communicable emerging or re-emerging disease. Implementing these measures, however, can inflict significant socio-economic and psychological costs. This paper presents a deterministic compartmental model for assessing the single and combined impact of quarantine and isolation to contain an epidemic. Comparisons are made with a mass vaccination program. The model is simulated using parameters for influenza-type diseases such as SARS. The study shows that even for an epidemic in which asymptomatic transmission does not occur, the quarantine of asymptomatically-infected individuals can be more effective than only isolating individuals with symptoms, if the associated reproductive number is high enough. For the case where asymptomatic transmission occurs, it is shown that isolation is more effective for a disease with a small basic reproduction number and transmission coefficient of asymptomatically-infected individuals. If asymptomatic individuals transmit at a rate that is at least 20% that of symptomatic individuals, quarantine is always more effective. The study further shows that the reduction in disease burden obtained from a combined quarantine and isolation program can be comparable to that obtained by a vaccination program, if the former is implemented quickly enough after the onset of the outbreak. If the implementation of such a quarantine/isolation program is delayed, however, even for a short while, its effectiveness decreases rapidly.

Download Full-text

A modelling study highlights the power of detecting and isolating asymptomatic or very mildly affected individuals for COVID-19 epidemic management

BMC Public Health ◽

10.1186/s12889-020-09843-7 ◽

2020 ◽

Vol 20 (1) ◽

Author(s):

Lía Mayorga ◽

Clara García Samartino ◽

Gabriel Flores ◽

Sofía Masuelli ◽

María V. Sánchez ◽

...

Keyword(s):

Compartmental Model ◽

Reproduction Number ◽

Mitigation Measures ◽

Asymptomatic Group ◽

Healthcare Burden ◽

Fundamental Part ◽

Management Policies ◽

Asymptomatic Individuals ◽

The Impact ◽

The Ideal

Abstract Background Mathematical modelling of infectious diseases is a powerful tool for the design of management policies and a fundamental part of the arsenal currently deployed to deal with the COVID-19 pandemic. Methods We present a compartmental model for the disease where symptomatic and asymptomatic individuals move separately. We introduced healthcare burden parameters allowing to infer possible containment and suppression strategies. In addition, the model was scaled up to describe different interconnected areas, giving the possibility to trigger regionalized measures. It was specially adjusted to Mendoza-Argentina’s parameters, but is easily adaptable for elsewhere. Results Overall, the simulations we carried out were notably more effective when mitigation measures were not relaxed in between the suppressive actions. Since asymptomatics or very mildly affected patients are the vast majority, we studied the impact of detecting and isolating them. The removal of asymptomatics from the infectious pool remarkably lowered the effective reproduction number, healthcare burden and overall fatality. Furthermore, different suppression triggers regarding ICU occupancy were attempted. The best scenario was found to be the combination of ICU occupancy triggers (on: 50%, off: 30%) with the detection and isolation of asymptomatic individuals. In the ideal assumption that 45% of the asymptomatics could be detected and isolated, there would be no need for complete lockdown, and Mendoza’s healthcare system would not collapse. Conclusions Our model and its analysis inform that the detection and isolation of all infected individuals, without leaving aside the asymptomatic group is the key to surpass this pandemic.

Download Full-text

The impact of asymptomatic individuals on the strength of public health interventions to prevent the second outbreak of COVID-19

10.21203/rs.3.rs-27142/v1 ◽

2020 ◽

Author(s):

Xiaochen Wang ◽

Shengfeng Wang ◽

Yueheng Lan ◽

Xiaofeng Tao ◽

Jinghua Xiao

Keyword(s):

Compartmental Model ◽

Economic Structure ◽

Health Interventions ◽

Control Measures ◽

Public Health Interventions ◽

Future Studies ◽

The Social ◽

Asymptomatic Individuals ◽

The Impact ◽

The Relationship

Abstract The pandemic of coronavirus disease 2019(COVID-19) has threatened the social and economic structure all around the world. Generally, COVID-19 has three possible transmission routes, including pre-symptomatic, symptomatic, and asymptomatic transmission, among which the last one has brought a severe challenge for the containment of the disease. One core scientific question is to understand the influence of asymptomatic individuals and of the strength of control measures on the evolution of the disease, particularly on a second outbreak of the disease. To explore these issues, we proposed a novel compartmental model that takes the infection of asymptomatic individuals into account. We get the relationship between asymptomatic individuals and critical strength of control measures theoretically. Furthermore, we verify the reliability of our model and the accuracy of the theoretical analysis by using the real confirmed cases of COVID-19 contamination. Our results, showing the importance of the asymptomatic population on the control measures, would provide useful theoretical reference to the policymakers and fuel future studies of COVID-19.

Download Full-text

A modelling study highlights the power of detecting and isolating asymptomatic or very mildly affected individuals for COVID-19 epidemic management.

10.21203/rs.3.rs-33492/v3 ◽

2020 ◽

Author(s):

Lia Mayorga ◽

Clara García Samartino ◽

Gabriel Flores ◽

Sofía Masuelli ◽

María V. Sánchez ◽

...

Keyword(s):

Compartmental Model ◽

Reproduction Number ◽

Mitigation Measures ◽

Asymptomatic Group ◽

Healthcare Burden ◽

Fundamental Part ◽

Management Policies ◽

Asymptomatic Individuals ◽

The Impact ◽

The Ideal

Abstract Background: Mathematical modelling of infectious diseases is a powerful tool for the design of management policies and a fundamental part of the arsenal currently deployed to deal with the COVID-19 pandemic. Methods: We present a compartmental model for the disease where symptomatic and asymptomatic individuals move separately. We introduced healthcare burden parameters allowing to infer possible containment and suppression strategies. In addition, the model was scaled up to describe different interconnected areas, giving the possibility to trigger regionalized measures. It was specially adjusted to Mendoza-Argentina’s parameters, but is easily adaptable for elsewhere. Results: Overall, the simulations we carried out were notably more effective when mitigation measures were not relaxed in between the suppressive actions. Since asymptomatics or very mildly affected patients are the vast majority, we studied the impact of detecting and isolating them. The removal of asymptomatics from the infectious pool remarkably lowered the effective reproduction number, healthcare burden and overall fatality. Furthermore, different suppression triggers regarding ICU occupancy were attempted. The best scenario was found to be the combination of ICU occupancy triggers (on: 50%, off: 30%) with the detection and isolation of asymptomatic individuals. In the ideal assumption that 45% of the asymptomatics could be detected and isolated, there would be no need for complete lockdown, and Mendoza’s healthcare system would not collapse. Conclusions: Our model and its analysis inform that the detection and isolation of all infected individuals, without leaving aside the asymptomatic group is the key to surpass this pandemic.

Download Full-text

A modelling study highlights the power of detecting and isolating asymptomatic or very mildly affected individuals for COVID-19 epidemic management.

10.21203/rs.3.rs-33492/v2 ◽

2020 ◽

Author(s):

Lia Mayorga ◽

Clara García Samartino ◽

Gabriel Flores ◽

Sofía Masuelli ◽

María V. Sánchez ◽

...

Keyword(s):

Compartmental Model ◽

Reproduction Number ◽

Mitigation Measures ◽

Asymptomatic Group ◽

Healthcare Burden ◽

Fundamental Part ◽

Management Policies ◽

Asymptomatic Individuals ◽

The Impact ◽

The Ideal

Download Full-text

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

International Journal of Biomathematics ◽

10.1142/s1793524511001726 ◽

2012 ◽

Vol 05 (04) ◽

pp. 1250029 ◽

Cited By ~ 3

Author(s):

S. MUSHAYABASA ◽

C. P. BHUNU

Keyword(s):

Deterministic Model ◽

Reproduction Number ◽

Positive Impact ◽

Transmission Dynamics ◽

Effective Control ◽

Reproductive Number ◽

Voluntary Testing ◽

Manifold Theory ◽

The Impact ◽

Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

Download Full-text

Estimating the burden of SARS-CoV-2 in France

Science ◽

10.1126/science.abc3517 ◽

2020 ◽

Vol 369 (6500) ◽

pp. 208-211 ◽

Cited By ~ 208

Author(s):

Henrik Salje ◽

Cécile Tran Kiem ◽

Noémie Lefrancq ◽

Noémie Courtejoie ◽

Paolo Bosetti ◽

...

Keyword(s):

Intensive Care ◽

Severe Acute Respiratory Syndrome ◽

Credible Interval ◽

Control Measures ◽

Reproductive Number ◽

Infected Population ◽

Population Immunity ◽

The Impact ◽

Second Wave ◽

Death Data

France has been heavily affected by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic and went into lockdown on 17 March 2020. Using models applied to hospital and death data, we estimate the impact of the lockdown and current population immunity. We find that 2.9% of infected individuals are hospitalized and 0.5% of those infected die (95% credible interval: 0.3 to 0.9%), ranging from 0.001% in those under 20 years of age to 8.3% in those 80 years of age or older. Across all ages, men are more likely to be hospitalized, enter intensive care, and die than women. The lockdown reduced the reproductive number from 2.90 to 0.67 (77% reduction). By 11 May 2020, when interventions are scheduled to be eased, we project that 3.5 million people (range: 2.1 million to 6.0 million), or 5.3% of the population (range: 3.3 to 9.3%), will have been infected. Population immunity appears to be insufficient to avoid a second wave if all control measures are released at the end of the lockdown.

Download Full-text

Modelling the Evolution of COVID-19 in High-Incidence European Countries and Regions: Estimated Number of Infections and Impact of Past and Future Intervention Measures

Journal of Clinical Medicine ◽

10.3390/jcm9061825 ◽

2020 ◽

Vol 9 (6) ◽

pp. 1825 ◽

Cited By ~ 3

Author(s):

Juan Fernández-Recio

Keyword(s):

Reproduction Number ◽

Mechanistic Model ◽

Control Measures ◽

European Countries ◽

Intervention Measures ◽

High Incidence ◽

Future Outcomes ◽

Long Term Impact ◽

The Impact

A previously developed mechanistic model of COVID-19 transmission has been adapted and applied here to study the evolution of the disease and the effect of intervention measures in some European countries and territories where the disease has had a major impact. A clear impact of the major intervention measures on the reproduction number (Rt) has been found in all studied countries and territories, as already suggested by the drop in the number of deaths over time. Interestingly, the impact of such major intervention measures seems to be the same in most of these countries. The model has also provided realistic estimates of the total number of infections, active cases and future outcomes. While the predictive capabilities of the model are much more uncertain before the peak of the outbreak, we could still reliably predict the evolution of the disease after a major intervention by assuming the subsequent reproduction number from the current study. A greater challenge is to foresee the long-term impact of softer intervention measures, but this model can estimate the outcome of different scenarios and help to plan changes for the implementation of control measures in a given country or region.

Download Full-text

Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies

Computational and Mathematical Methods in Medicine ◽

10.1155/2020/8869377 ◽

2020 ◽

Vol 2020 ◽

pp. 1-21

Author(s):

Aristide G. Lambura ◽

Gasper G. Mwanga ◽

Livingstone Luboobi ◽

Dmitry Kuznetsov

Keyword(s):

Optimal Control ◽

Equilibrium Point ◽

Drug Administration ◽

Mass Drug Administration ◽

Helminth Infection ◽

Reproduction Number ◽

Control Strategies ◽

Active Tuberculosis ◽

Control Measures ◽

The Impact

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

Download Full-text

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

10.1101/2020.05.16.20104471 ◽

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.

Download Full-text

Investigating the impact of vaccination and non-pharmaceutical measures in curbing COVID-19 spread: A South Africa perspective

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2022049 ◽

2021 ◽

Vol 19 (1) ◽

pp. 1058-1077

Author(s):

Shina D. Oloniiju ◽

◽

Olumuyiwa Otegbeye ◽

Absalom E. Ezugwu ◽

◽

...

Keyword(s):

Reproduction Number ◽

Transmission Probability ◽

Control Measures ◽

World Population ◽

Reproduction Rate ◽

Secondary Infections ◽

Perform Sensitivity Analysis ◽

African Context ◽

The Impact ◽

Effective Reaction

<abstract><p>The year 2020 brought about a pandemic that caught most of the world population by surprise and wreaked unimaginable havoc before any form of effective reaction could be put in place. COVID-19 is proving to be an epidemic that keeps on having an upsurge whenever it looks like it is being curbed. This pandemic has led to continuous strategizing on approaches to quelling the surge. The recent and welcome introduction of vaccines has led to renewed optimism for the population at large. The introduction of vaccines has led to the need to investigate the effect of vaccination among other control measures in the fight against COVID-19. In this study, we develop a mathematical model that captures the dynamics of the disease taking into consideration some measures that are easier to implement majorly within the African context. We consider quarantine and vaccination as control measures and investigate the efficacy of these measures in curbing the reproduction rate of the disease. We analyze the local stability of the disease-free equilibrium point. We also perform sensitivity analysis of the effective reproduction number to determine which parameters significantly lowers the effective reproduction number. The results obtained suggest that quarantine and a vaccine with at least $ 75\% $ efficacy and reducing transmission probability through sanitation and wearing of protective gears can significantly reduce the number of secondary infections.</p></abstract>

Download Full-text