Applied & Industrial Mathematics
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Browsing Applied & Industrial Mathematics by Subject "Disease modelling"
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Item Open Access Dynamics of Naive and Memory CD4 T-cells in Chronically Infected HIV Patients Post-Injection of Down-Modulated CCR5 Memory CD4-Cells(2016-11-25) Raad, Angie; Heffernan, Jane M.HIV/AIDS, a sexually transmitted diseases continues to affect the lives of millions of individuals worldwide. This retrovirus targets CD4 T-cell populations, the main driver of the immune system by using the chemokine co-receptor 5 (CCR5). Despite the success of the highly active antiretroviral therapy in reconstituting the immune system, HIV infected individuals still suffer from low CD4 T-cell counts. Recently, researchers were able to highlight the success of immunotherapy in restoring the CD4 T-cell count. To further, investigate such importance, our collaborators at case Western University injected CCR5-down-modulated memory CD4 T-cells into 9 chronically infected HIV patients. Using a linear transitions from the naive to the effector memory state, a non linear ordinary differential equation model was used to model the experiment. Various data fitting techniques in Matlab Stan and Monolix software were used to estimate the model parameters (proliferation, death, transition and birth rates) before and after the initiation of the treatment to study the change of the cell dynamics. Our fittings have indicated an increase in the memory stem and na\"{\i}ve cell lifespan post-clinical trial. Using sensitivity analysis, we showed that the na\"{\i}ve cell birth rate from the thymus lambda, the memory stem cell proliferation rate p_ST and the central memory cell death rate d_C played an important role in restoring the CD4 T-cell count. A stochastic model for the CD4 T-cells population was developed to examine if fluctuations from the stochastic simulation were able to capture the experimental data measurements. The findings of this study indicates the importance of looking further into how modified CD4 T-cells are able to restore the T-cell counts which thereby decrease the HIV virus pool and help HIV patients to maintain a low level of the virus and most importantly a high level of T-cell count.Item Open Access The Impact of Population Heterogeneities and Disease Interventions on Herd Immunity: A Case Study of the COVID-19 Pandemic in Ontario(2023-03-28) Liwag, Maria Geneva Roselle Marino; Moghadas, SeyedIn epidemiology, herd immunity refers to the population level of immunity required to prevent or extinguish a large disease outbreak. In models with homogeneously mixing assumptions and without demographic structures, the herd immunity level may be different from that in heterogeneous models. With the COVID-19 pandemic in Ontario as a case study, a comprehensive deterministic mathematical model of disease spread with age and contact pattern variations was developed to examine the required herd immunity for different variants and compare with theoretical values obtained using homogeneous assumptions. The effects of non-pharmaceutical (testing/isolation of silent infections) interventions and vaccination on epidemic progression and herd immunity were investigated. With the inclusion of age and contact pattern structures, the resulting herd immunity level required to end an epidemic under the assumptions of long-term protection (without re-infection) is lower than theoretical values, even for more transmissible variants. While waning immunity and re-infection results in an oscillation in herd immunity levels in the population, subsequent epidemic peaks are less amplified, suggesting that even with increased variant transmissibility, infections of any variant allow for population immunity to rise, leading to an endemic state.