In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniquene...In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.展开更多
Throughout the progress of epidemic scenarios,individuals in different health classes are expected to have different average daily contact behavior.This contact heterogeneity has been studied in recent adaptive models...Throughout the progress of epidemic scenarios,individuals in different health classes are expected to have different average daily contact behavior.This contact heterogeneity has been studied in recent adaptive models and allows us to capture the inherent differences across health statuses better.Diseases with reinfection bring out more complex scenarios and offer an important application to consider contact disaggregation.Therefore,we developed a nonlinear differential equation model to explore the dynamics of relapse phenomena and contact differences across health statuses.Our incidence rate function is formulated,taking inspiration from recent adaptive algorithms.It incorporates contact behavior for individuals in each health class.We use constant contact rates at each health status for our analytical results and prove conditions for different forward-backward bifurcation scenarios.The relationship between the different contact rates heavily in-fluences these conditions.Numerical examples highlight the effect of temporarily recov-ered individuals and initial conditions on infected population persistence.展开更多
Tuberculosis(TB)continues to disproportionately affect Inuit populations in Canada with some communities having over 300 times higher rate of active TB than Canadian-born,non-Indigenous people.Inuit Tuberculosis Elimi...Tuberculosis(TB)continues to disproportionately affect Inuit populations in Canada with some communities having over 300 times higher rate of active TB than Canadian-born,non-Indigenous people.Inuit Tuberculosis Elimination Framework has set the goal of reducing active TB incidence by at least 50%by 2025,aiming to eliminate it by 2030.Whether these goals are achievable with available resources and treatment regimens currently in practice has not been evaluated.We developed an agent-based model of TB transmission to evaluate timelines and milestones attainable in Nunavut,Canada by including case findings,contact-tracing and testing,treatment of latent TB infection(LTBI),and the government investment on housing infrastructure to reduce the average house-hold size.The model was calibrated to ten years of TB incidence data,and simulated for 20 years to project program outcomes.We found that,under a range of plausible scenarios with tracing and testing of 25%e100%of frequent contacts of detected active cases,the goal of 50%reduction in annual incidence by 2025 is not achievable.If active TB cases are identified rapidly within one week of becoming symptomatic,then the annual incidence would reduce below 100 per 100,000 population,with 50%reduction being met between 2025 and 2030.Eliminating TB from Inuit populations would require high rates of contacttracing and would extend beyond 2030.The findings indicate that time-to-identification of active TB is a critical factor determining program effectiveness,suggesting that investment in resources for rapid case detection is fundamental to controlling TB.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10471022, 10771032)Natural Science Foundation of Jiangsu Province (Grant No. BK2006088)
文摘In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.
基金support from the Research Center in Pure and Applied Mathematics and the Department of Mathematics at Universidad de Costa Rica.
文摘Throughout the progress of epidemic scenarios,individuals in different health classes are expected to have different average daily contact behavior.This contact heterogeneity has been studied in recent adaptive models and allows us to capture the inherent differences across health statuses better.Diseases with reinfection bring out more complex scenarios and offer an important application to consider contact disaggregation.Therefore,we developed a nonlinear differential equation model to explore the dynamics of relapse phenomena and contact differences across health statuses.Our incidence rate function is formulated,taking inspiration from recent adaptive algorithms.It incorporates contact behavior for individuals in each health class.We use constant contact rates at each health status for our analytical results and prove conditions for different forward-backward bifurcation scenarios.The relationship between the different contact rates heavily in-fluences these conditions.Numerical examples highlight the effect of temporarily recov-ered individuals and initial conditions on infected population persistence.
基金support from Natural Sciences and Engineering Research Council of Canada through Individual Discovery Grant.
文摘Tuberculosis(TB)continues to disproportionately affect Inuit populations in Canada with some communities having over 300 times higher rate of active TB than Canadian-born,non-Indigenous people.Inuit Tuberculosis Elimination Framework has set the goal of reducing active TB incidence by at least 50%by 2025,aiming to eliminate it by 2030.Whether these goals are achievable with available resources and treatment regimens currently in practice has not been evaluated.We developed an agent-based model of TB transmission to evaluate timelines and milestones attainable in Nunavut,Canada by including case findings,contact-tracing and testing,treatment of latent TB infection(LTBI),and the government investment on housing infrastructure to reduce the average house-hold size.The model was calibrated to ten years of TB incidence data,and simulated for 20 years to project program outcomes.We found that,under a range of plausible scenarios with tracing and testing of 25%e100%of frequent contacts of detected active cases,the goal of 50%reduction in annual incidence by 2025 is not achievable.If active TB cases are identified rapidly within one week of becoming symptomatic,then the annual incidence would reduce below 100 per 100,000 population,with 50%reduction being met between 2025 and 2030.Eliminating TB from Inuit populations would require high rates of contacttracing and would extend beyond 2030.The findings indicate that time-to-identification of active TB is a critical factor determining program effectiveness,suggesting that investment in resources for rapid case detection is fundamental to controlling TB.
