The state-reproduction number for a multistate class age structured epidemic system and its application to the asymptomatic transmission model

AbstractThe role of school-based contacts in the epidemiology of SARS-CoV-2 is incompletely understood. We use an age-structured transmission model fitted to age-specific seroprevalence and hospital admission data to assess the effects of school-based measures at different time points during the COVID-19 pandemic in the Netherlands. Our analyses suggest that the impact of measures reducing school-based contacts depends on the remaining opportunities to reduce non-school-based contacts. If opportunities to reduce the effective reproduction number (Re) with non-school-based measures are exhausted or undesired and Re is still close to 1, the additional benefit of school-based measures may be considerable, particularly among older school children. As two examples, we demonstrate that keeping schools closed after the summer holidays in 2020, in the absence of other measures, would not have prevented the second pandemic wave in autumn 2020 but closing schools in November 2020 could have reduced Re below 1, with unchanged non-school-based contacts.

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Model-based evaluation of school- and non-school-related measures to control the COVID-19 pandemic

10.21203/rs.3.rs-130264/v1 ◽

2021 ◽

Author(s):

Ganna Rozhnova ◽

Christiaan van Dorp ◽

Patricia Bruijning-Verhagen ◽

Martin Bootsma ◽

Janneke van de Wijgert ◽

...

Keyword(s):

Reproduction Number ◽

Additional Benefit ◽

Transmission Model ◽

Time Points ◽

School Based ◽

Admission Data ◽

Age Structured ◽

The Impact ◽

Pandemic Wave

Abstract The role of school-based contacts in the epidemiology of SARS-CoV-2 is incompletely understood. We used an age-structured transmission model fitted to age-specific seroprevalence and hospital admission data to assess the effects of school-based measures at different time points during the COVID-19 pandemic in the Netherlands. Our analyses suggest that the impact of measures reducing school-based contacts depends on the remaining opportunities to reduce non-school-based contacts. If opportunities to reduce the effective reproduction number (Re) with non-school-based measures are exhausted or undesired and Re is still close to 1, the additional benefit of school-based measures may be considerable, particularly among older school children. As two examples, we demonstrate that keeping schools closed after the summer holidays in 2020, in the absence of other measures, would not have prevented the second pandemic wave in autumn 2020 but closing schools in November 2020 could have reduced Re below 1, with unchanged non-school-based contacts.

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Dynamics of an Age Structured Heroin Transmission Model with Imperfect Vaccination

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421501571 ◽

2021 ◽

Vol 31 (10) ◽

pp. 2150157

Author(s):

Xi-Chao Duan ◽

Huanhuan Cheng ◽

Maia Martcheva ◽

Sanling Yuan

Keyword(s):

Steady State ◽

Reproduction Number ◽

Transmission Model ◽

Well Posedness ◽

Special Cases ◽

Positive Steady States ◽

State Formula ◽

Number Formula ◽

Age Structured ◽

Drug Free

In this paper, we formulate a new-age structured heroin transmission model with respect to the age of vaccination which structures the vaccine wanes rate [Formula: see text] and infection ratio of vaccination individuals [Formula: see text]. The well-posedness and the basic reproduction number [Formula: see text] of our model are first presented. If [Formula: see text], the drug-free steady state [Formula: see text] is locally stable and there will be multiple positive steady states due to the imperfect vaccine. If [Formula: see text], there is a unique drug spread steady state, and our model is uniformly persistent. To reveal the dynamics of our model in detail, we carry out a further analysis in some special cases, including the backward and forward bifurcation results of our model when [Formula: see text] and [Formula: see text], and the unique drug-spread steady state’s stability when [Formula: see text]. Finally, a brief conclusion and discussion are presented.

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A Class Age-Structured HIV/AIDS Model with Impulsive Drug-Treatment Strategy

Discrete Dynamics in Nature and Society ◽

10.1155/2010/758745 ◽

2010 ◽

Vol 2010 ◽

pp. 1-12 ◽

Cited By ~ 6

Author(s):

Helong Liu ◽

Lianbing Li

Keyword(s):

Drug Treatment ◽

Antiretroviral Treatment ◽

Impulsive Differential Equations ◽

The State ◽

Transmission Model ◽

Effective Vaccine ◽

Infection Age ◽

Aids Epidemic ◽

Age Structured ◽

Hiv Aids

We formulate an HIV/AIDS transmission model that considers the dependence of HIV/AIDS progress on infection age (the time since infection), disease age (the time elapsed since the onset), and impulsive antiretroviral treatment. Since no effective vaccine is available for HIV/AIDS, our impulsive disease-control strategy is targeted at infected individuals (I control). Thus the model only includes infective class and AIDS class: infected population is the state at birth, and AIDS population is not the state at birth. Assuming the theoretical strategy can provide HIV testing for risk population groups every years and immediate antiretroviral treatment for HIV-positive people. The action is approximated by impulsive differential equations. We demonstrate the effect of the impulsive drug treatment and show that there exists a globally stable infection-free state when the impulsive period and drug-treatment proportion satisfy . This result shows that the prevention effects can drive HIV/AIDS epidemic towards to elimination.

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The effects of non-pharmaceutical interventions on SARS-CoV-2 transmission in different socioeconomic populations in Kuwait: a modeling study

BMC Public Health ◽

10.1186/s12889-021-10984-6 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Fatima Khadadah ◽

Abdullah A. Al-Shammari ◽

Ahmad Alhashemi ◽

Dari Alhuwail ◽

Bader Al-Saif ◽

...

Keyword(s):

Disease Transmission ◽

Reproduction Number ◽

Transmission Model ◽

Socioeconomic Groups ◽

Before And After ◽

Cross Transmission ◽

Community Transmission ◽

The Impact ◽

Pharmaceutical Interventions ◽

The Basic Reproduction Number

Abstract Background Aggressive non-pharmaceutical interventions (NPIs) may reduce transmission of SARS-CoV-2. The extent to which these interventions are successful in stopping the spread have not been characterized in countries with distinct socioeconomic groups. We compared the effects of a partial lockdown on disease transmission among Kuwaitis (P1) and non-Kuwaitis (P2) living in Kuwait. Methods We fit a modified metapopulation SEIR transmission model to reported cases stratified by two groups to estimate the impact of a partial lockdown on the effective reproduction number ($$ {\mathcal{R}}_e $$ R e ). We estimated the basic reproduction number ($$ {\mathcal{R}}_0 $$ R 0 ) for the transmission in each group and simulated the potential trajectories of an outbreak from the first recorded case of community transmission until 12 days after the partial lockdown. We estimated $$ {\mathcal{R}}_e $$ R e values of both groups before and after the partial curfew, simulated the effect of these values on the epidemic curves and explored a range of cross-transmission scenarios. Results We estimate $$ {\mathcal{R}}_e $$ R e at 1·08 (95% CI: 1·00–1·26) for P1 and 2·36 (2·03–2·71) for P2. On March 22nd, $$ {\mathcal{R}}_e $$ R e for P1 and P2 are estimated at 1·19 (1·04–1·34) and 1·75 (1·26–2·11) respectively. After the partial curfew had taken effect, $$ {\mathcal{R}}_e $$ R e for P1 dropped modestly to 1·05 (0·82–1·26) but almost doubled for P2 to 2·89 (2·30–3·70). Our simulated epidemic trajectories show that the partial curfew measure greatly reduced and delayed the height of the peak in P1, yet significantly elevated and hastened the peak in P2. Modest cross-transmission between P1 and P2 greatly elevated the height of the peak in P1 and brought it forward in time closer to the peak of P2. Conclusion Our results indicate and quantify how the same lockdown intervention can accentuate disease transmission in some subpopulations while potentially controlling it in others. Any such control may further become compromised in the presence of cross-transmission between subpopulations. Future interventions and policies need to be sensitive to socioeconomic and health disparities.

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Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England

Science ◽

10.1126/science.abg3055 ◽

2021 ◽

Vol 372 (6538) ◽

pp. eabg3055 ◽

Cited By ~ 82

Author(s):

Nicholas G. Davies ◽

Sam Abbott ◽

Rosanna C. Barnard ◽

Christopher I. Jarvis ◽

Adam J. Kucharski ◽

...

Keyword(s):

United States ◽

Severe Acute Respiratory Syndrome ◽

Reproduction Number ◽

The United States ◽

Control Measures ◽

Transmission Model ◽

Educational Institutions ◽

Stringent Control ◽

Dynamic Transmission Model ◽

Credible Intervals

A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant, VOC 202012/01 (lineage B.1.1.7), emerged in southeast England in September 2020 and is rapidly spreading toward fixation. Using a variety of statistical and dynamic modeling approaches, we estimate that this variant has a 43 to 90% (range of 95% credible intervals, 38 to 130%) higher reproduction number than preexisting variants. A fitted two-strain dynamic transmission model shows that VOC 202012/01 will lead to large resurgences of COVID-19 cases. Without stringent control measures, including limited closure of educational institutions and a greatly accelerated vaccine rollout, COVID-19 hospitalizations and deaths across England in the first 6 months of 2021 were projected to exceed those in 2020. VOC 202012/01 has spread globally and exhibits a similar transmission increase (59 to 74%) in Denmark, Switzerland, and the United States.

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Mathematical Analysis of an Immune-structured Hikungunya Transmission Model

European Journal of Pure and Applied Mathematics ◽

10.29020/nybg.ejpam.v12i4.3532 ◽

2019 ◽

Vol 12 (4) ◽

pp. 1533-1552

Author(s):

Kambire Famane ◽

Gouba Elisée ◽

Tao Sadou ◽

Blaise Some

Keyword(s):

Numerical Simulation ◽

Asymptotic Stability ◽

Deterministic Model ◽

Reproduction Number ◽

Transmission Model ◽

Acquired Immunity ◽

Local Asymptotic Stability ◽

Well Posed ◽

Disease Free ◽

The Basic Reproduction Number

In this paper, we have formulated a new deterministic model to describe the dynamics of the spread of chikunguya between humans and mosquitoes populations. This model takes into account the variation in mortality of humans and mosquitoes due to other causes than chikungunya disease, the decay of acquired immunity and the immune sytem boosting. From the analysis, itappears that the model is well posed from the mathematical and epidemiological standpoint. The existence of a single disease free equilibrium has been proved. An explicit formula, depending on the parameters of the model, has been obtained for the basic reproduction number R0 which is used in epidemiology. The local asymptotic stability of the disease free equilibrium has been proved. The numerical simulation of the model has confirmed the local asymptotic stability of the diseasefree equilbrium and the existence of endmic equilibrium. The varying effects of the immunity parameters has been analyzed numerically in order to provide better conditions for reducing the transmission of the disease.

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Mathematical Models for Assessing Vaccination Scenarios in Several Provinces in Indonesia

10.1101/2020.12.21.20248241 ◽

2020 ◽

Author(s):

N. Nuraini ◽

K. Khairudin ◽

P. Hadisoemarto ◽

H. Susanto ◽

A. Hasan ◽

...

Keyword(s):

Mathematical Models ◽

Age Groups ◽

Transmission Model ◽

West Java ◽

Dynamic Transmission Model ◽

Simulation Results ◽

Age Structured

AbstractTo mitigate more casualties from the COVID-19 outbreak, this study assessed optimal vaccination scenarios, considering some existing healthcare conditions and some assumptions, by developing SIQRD (Susceptible-Infected-Quarantine-Recovery-Death) models for Jakarta, West Java, and Banten, in Indonesia. The models included an age-structured dynamic transmission model that naturally could give different treatments among age groups of population. The simulation results show that the timing and period’s length of the vaccination should be well planned and prioritizing particular age groups will give significant impact on the total number of casualties.

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Global dynamics of a Huanglongbing model with a periodic latent period

Discrete and Continuous Dynamical Systems - Series B ◽

10.3934/dcdsb.2021302 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Yan Hong ◽

Xiuxiang Liu ◽

Xiao Yu

Keyword(s):

Reproduction Number ◽

Threshold Value ◽

Transmission Model ◽

Threshold Dynamics ◽

Global Dynamics ◽

Temperature Dependent ◽

Candidatus Liberibacter ◽

Effects Of Temperature ◽

Disease Free ◽

The Basic Reproduction Number

<p style='text-indent:20px;'>Huanglongbing (HLB) is a disease of citrus that caused by phloem-restricted bacteria of the Candidatus Liberibacter group. In this paper, we present a HLB transmission model to investigate the effects of temperature-dependent latent periods and seasonality on the spread of HLB. We first establish disease free dynamics in terms of a threshold value <inline-formula><tex-math id="M1">\begin{document}$ R^p_0 $\end{document}</tex-math></inline-formula>, and then introduce the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> and show the threshold dynamics of HLB with respect to <inline-formula><tex-math id="M3">\begin{document}$ R^p $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>. Numerical simulations are further provided to illustrate our analytic results.</p>

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The Role of Migration in Maintaining the Transmission of Avian Influenza in Waterfowl: A Multisite Multispecies Transmission Model along East Asian-Australian Flyway

Canadian Journal of Infectious Diseases and Medical Microbiology ◽

10.1155/2018/3420535 ◽

2018 ◽

Vol 2018 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Akira Endo ◽

Hiroshi Nishiura

Keyword(s):

Avian Influenza ◽

Reproduction Number ◽

Transmission Rate ◽

Temporal Variations ◽

Transmission Model ◽

Global Dynamics ◽

Long Distance ◽

Transmission Potential ◽

Influenza Transmission

Background. Migratory waterfowl annually migrate over the continents along the routes known as flyways, serving as carriers of avian influenza virus across distant locations. Prevalence of influenza varies with species, and there are also geographical and temporal variations. However, the role of long-distance migration in multispecies transmission dynamics has yet to be understood. We constructed a mathematical model to capture the global dynamics of avian influenza, identifying species and locations that contribute to sustaining transmission.Methods. We devised a multisite, multispecies SIS (susceptible-infectious-susceptible) model, and estimated transmission rates within and between species in each geographical location from prevalence data. Parameters were directly sampled from posterior distribution under Bayesian inference framework. We then analyzed contribution of each species in each location to the global patterns of influenza transmission.Results. Transmission and migration parameters were estimated by Bayesian posterior sampling. The basic reproduction number was estimated at 1.1, slightly above the endemic threshold. Mallard was found to be the most important host with the highest transmission potential, and high- and middle-latitude regions appeared to act as hotspots of influenza transmission. The local reproduction number suggested that the prevalence of avian influenza in the Oceania region is dependent on the inflow of infected birds from other regions.Conclusion. Mallard exhibited the highest transmission rate among the species explored. Migration was suggested to be a key factor of the global prevalence of avian influenza, as transmission is locally sustainable only in the northern hemisphere, and the virus could be extinct in the Oceania region without migration.

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