Mathematical modeling and analysis for controlling the spread of infectious diseases

Tyagi, Swati; Martha, S. C.; Abbas, Syed; Debbouche, Amar

doi:10.1016/j.chaos.2021.110707

Cited by 35 publications

(19 citation statements)

References 33 publications

(25 reference statements)

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“…The time dependence of infected individuals in a community can show a multitude of behavior including wavy patterns such as secondary waves and insurgences. To formulate different countermeasures against the spread of the virus, it is desirable to use mathematical models to produce the predictive results [ 28 , 29 , 34 , 44 , 46 ]. These models prove to be effective tools to study, explain and more importantly, forecast the future trajectory of the spread of the virus and of its variants, under different scenarios in states, countries or groups of individuals [ 2 , 15 , 20 ].…”

Section: Discussionmentioning

confidence: 99%

“…In the context of the current situation worldwide, appropriate epidemic models [ 13 , 14 , 28 , 29 , 33 , 34 , 39 , 44 , 46 ] for the prediction of the spread of COVID-19 in different countries and communities are highly relevant and important. In particular, the SIR model and its extended modifications [ 17 – 19 , 48 ], such as the extended SIR model in various forms, have been used in previous studies [ 30 , 35 ] to model the spread of COVID-19 in communities.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

et al. 2022

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In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptible–infected–removed (SIR) model and can track the evolution of infections in communities, i.e., in countries, states or groups of individuals, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the effective transmission and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as it can estimate the effective infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter information can be used to forecast the future basic reproduction number and together with the forecast on the number of infected and dead individuals, our approach can further be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This, in conjunction with the implementation of vaccination programs worldwide, can help reduce significantly the impact of the spread around the world and improve the wellbeing of people.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

et al. 2022

View full text Add to dashboard Cite

show abstract

“…The time dependence of infected individuals in a community can show a multitude of behavior including wavy patterns such as secondary waves and insurgences. To formulate different countermeasures against the spread of the virus, it is desirable to use mathematical models to produce predictive results [24,25,40,30,42]. These models prove to be effective tools to study, explain and more importantly, forecast the future trajectory of the spread of the virus and of its variants, under different scenarios in states, countries or groups of individuals [14,19,2].…”

Section: Discussionmentioning

confidence: 99%

“…In the context of the current situation worldwide, appropriate epidemic models [24,25,13,35,12,40,29,30,42] for the prediction of the spread of COVID-19 in different countries and communities are highly relevant and important. In particular, the SIR model and its extended modifications [16,17,18,47], such as the extended SIR model in various forms have been used in previous studies [26,31] to model the spread of COVID-19 in communities.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

Cooper¹,

Mondal²,

Antonopoulos³

et al. 2022

Preprint

View full text Add to dashboard Cite

In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptibleinfected-removed (SIR) model and can track the evolution of infections in communities, i.e., in countries, states or groups of individuals, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the effective transmission and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as it can estimate the effective infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter information can be used to forecast the future basic reproduction number and together with the forecast on the number of infected and dead individuals, our approach can further be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This, in conjunction with the implementation of vaccination programs worldwide, can help reduce significantly the impact of the spread around the world and improve the wellbeing of people.

show abstract

“…In the context of the current situation worldwide, appropriate epidemic models [23,24,13,34,12,39,28,29,41] for the prediction of the spread of COVID-19 in countries and communities are highly relevant and important. In particular, the SIR model and its extended modifications [16][17][18]46], such as the extended SIR model in various forms have been used in previous studies [25,30] to model the spread of COVID-19 in communities.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

Cooper

Mondal

Antonopoulos

et al. 2021

Preprint

View full text Add to dashboard Cite

In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptible-infected-removed (SIR) model and can track the evolution of infections in communities, i.e., in countries, states or groups of individuals, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the probability of the infection and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan in the end of August 2021, assuming a major outbreak occurs in early August 2021 in India and in mid-July 2021 in Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as to estimate the probability of the infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter information can be used to forecast the future basic reproduction number and together with the forecast on the number of infected and dead individuals, our approach can further be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This, in conjunction with the implementation of vaccination programs worldwide, can help reduce significantly the impact of the spread around the world and improve the wellbeing of people.

show abstract

Mathematical modeling and analysis for controlling the spread of infectious diseases

Cited by 35 publications

References 33 publications

Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

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