In this paper, we build an epidemiological model to investigate the dynamics of the spread of dengue fever in human population. We apply optimal control theory via the Pontryagins Minimum Principle together with the R...In this paper, we build an epidemiological model to investigate the dynamics of the spread of dengue fever in human population. We apply optimal control theory via the Pontryagins Minimum Principle together with the Runge-Kutta solution technique to a “simple” SEIRS disease model. Controls representing education and drug therapy treatment are incorporated to reduce the latently infected and actively infected individual populations. The overall thrust is the minimization of the spread of the disease in a population by adopting an optimization technique as a guideline.展开更多
We propose and analyze an epidemiological model to evaluate the effectiveness of bed nets as a prophylactic measure in malaria-endemic areas. The main purpose in this work is the modeling of the aggressiveness of anop...We propose and analyze an epidemiological model to evaluate the effectiveness of bed nets as a prophylactic measure in malaria-endemic areas. The main purpose in this work is the modeling of the aggressiveness of anopheles mosquitoes relative to the way humans use to protect themselves against bites of mosquitoes. This model is a system of several differential equations: the number of equations depends on the particular assumptions of the model. We compute the basic reproduction number, and show that if, the disease free equilibrium (DFE) is globally asymptotically stable on the non-negative orthant. If, the system admits a unique endemic equilibrium (EE) that is globally and asymptotically stable. Numerical simulations are presented corresponding to scenarios typical of malaria-endemic areas, based on data collected in the literature. Finally, we discuss the relative effectiveness of different kinds of bed nets.展开更多
In India, the most common cancer among men is cancer of lip-oral and its incidence is further increasing. Nodal metastasis is an important prognostic factor in oral cancer. Previous studies on factors associated with ...In India, the most common cancer among men is cancer of lip-oral and its incidence is further increasing. Nodal metastasis is an important prognostic factor in oral cancer. Previous studies on factors associated with nodal involvement are mainly focused on clinical exploration, and there is very little work in statistical modeling for nodal involvement. Also, the available studies have limited covariates and their varying forms. Further, studies available from India have mainly focused either on occult nodal metastasis only or a specific site of oral or stages. Hence, in order to identify epidemiological determinants of nodal metastasis, objective of this study was to develop a regression model to find out factors associated with nodal involvement and assess its validity. 945 histopathologically proven oral squamous cell carcinoma (OSCC) patients who went under surgery including neck dissection during 1995-2013 at the Department of Surgical Oncology, Dr. BRA-IRCH, AIIMS, New Delhi, India, were included for model building. Another data of 204 patients available during 2014-2015 was used for the temporal validation of the developed model. To assess the factors associated with nodal involvement, stepwise multivariable logistic regression procedure was used and results are presented as odds ratio and corresponding 95% confidence interval (CI). Pain at the time of presentation [1.34 (1.02 to 1.77)], sub mucous fibrosis (SMF) [0.45 (0.21 to 0.95)], palpable neck node [2.38 (1.69 to 3.35)], tongue [1.63 (1.07 to 2.46)] as compared to buccal mucosa and degree of differentiation [1.41 (1.05 to 1.89)] were found to be significantly associated with nodal involvement. Further, diagnostic performance of the developed model was found to be satisfactory on temporal validation. These data suggest that, Pain at time of presentation, presence of clinical neck node, SMF, degree of differentiation and oral site are the most probable factors associated with nodal involvement in OSCC.展开更多
文摘In this paper, we build an epidemiological model to investigate the dynamics of the spread of dengue fever in human population. We apply optimal control theory via the Pontryagins Minimum Principle together with the Runge-Kutta solution technique to a “simple” SEIRS disease model. Controls representing education and drug therapy treatment are incorporated to reduce the latently infected and actively infected individual populations. The overall thrust is the minimization of the spread of the disease in a population by adopting an optimization technique as a guideline.
文摘We propose and analyze an epidemiological model to evaluate the effectiveness of bed nets as a prophylactic measure in malaria-endemic areas. The main purpose in this work is the modeling of the aggressiveness of anopheles mosquitoes relative to the way humans use to protect themselves against bites of mosquitoes. This model is a system of several differential equations: the number of equations depends on the particular assumptions of the model. We compute the basic reproduction number, and show that if, the disease free equilibrium (DFE) is globally asymptotically stable on the non-negative orthant. If, the system admits a unique endemic equilibrium (EE) that is globally and asymptotically stable. Numerical simulations are presented corresponding to scenarios typical of malaria-endemic areas, based on data collected in the literature. Finally, we discuss the relative effectiveness of different kinds of bed nets.
文摘In India, the most common cancer among men is cancer of lip-oral and its incidence is further increasing. Nodal metastasis is an important prognostic factor in oral cancer. Previous studies on factors associated with nodal involvement are mainly focused on clinical exploration, and there is very little work in statistical modeling for nodal involvement. Also, the available studies have limited covariates and their varying forms. Further, studies available from India have mainly focused either on occult nodal metastasis only or a specific site of oral or stages. Hence, in order to identify epidemiological determinants of nodal metastasis, objective of this study was to develop a regression model to find out factors associated with nodal involvement and assess its validity. 945 histopathologically proven oral squamous cell carcinoma (OSCC) patients who went under surgery including neck dissection during 1995-2013 at the Department of Surgical Oncology, Dr. BRA-IRCH, AIIMS, New Delhi, India, were included for model building. Another data of 204 patients available during 2014-2015 was used for the temporal validation of the developed model. To assess the factors associated with nodal involvement, stepwise multivariable logistic regression procedure was used and results are presented as odds ratio and corresponding 95% confidence interval (CI). Pain at the time of presentation [1.34 (1.02 to 1.77)], sub mucous fibrosis (SMF) [0.45 (0.21 to 0.95)], palpable neck node [2.38 (1.69 to 3.35)], tongue [1.63 (1.07 to 2.46)] as compared to buccal mucosa and degree of differentiation [1.41 (1.05 to 1.89)] were found to be significantly associated with nodal involvement. Further, diagnostic performance of the developed model was found to be satisfactory on temporal validation. These data suggest that, Pain at time of presentation, presence of clinical neck node, SMF, degree of differentiation and oral site are the most probable factors associated with nodal involvement in OSCC.
