RESUMO
In order to describe mathematically the transmission of microparasites, especially directly transmitted infections, it is usual to set up differential equations assuming the mass action law and a homogeneously mixed population. In this paper we analyze such a model taking into account heterogeneity with respect to the infectivity, that is, the variability in the evolution of the interaction between parasite and the human host during the infectious period. The well established biological phenomenon of initial increase in parasite abundance followed by its decrease, due to the interaction between the host's immunological response and the parasite, has thus been taken into account. The variable amount of microparasites eliminated by an infectious individual, and the different (heterogeneous) immunological response build up by the host when in interaction with parasite are present in the model. The analytical expression for the basic reproduction ratio is derived through stability analysis.
Assuntos
Transmissão de Doença Infecciosa/estatística & dados numéricos , Modelos Imunológicos , Carga Viral/estatística & dados numéricos , Viroses/transmissão , Infecções por HIV/imunologia , Infecções por HIV/transmissão , Hepatite B/imunologia , Hepatite B/transmissão , Interações Hospedeiro-Parasita , Humanos , Tuberculose/imunologia , Tuberculose/transmissão , Viroses/imunologia , Vírus/crescimento & desenvolvimentoRESUMO
This paper presents a diffusion model of larval dispersal especifically designed to account for particular aspects of postfeeding larval dispersal from the food source in organisms such as blowflies. In these organisms the dispersal of immatures includes two groups of individuals, those that are actively migrating and those that initiated the pupation process. The classical diffusion equation in one dimension was modified to incorporate a function which describes the burying of larvae to become pupae. The analytical solution of this equation predicts oscillatory and monotonic dispersal behaviors, which are observed in experimental populations of blowfly species.
Assuntos
Animais , Dípteros/embriologia , Larva/fisiologiaRESUMO
This paper presents a diffusion model of larval dispersal specifically designed to account for particular aspects of postfeeding larval dispersal from the food source in organisms such as blowflies. In these organisms the dispersal of immatures includes two groups of individuals, those that are actively migrating and those that have initiated the pupation process. The classical diffusion equation in one dimension was modified to incorporate a function which describes the burying of larvae to become pupae. The analytical solution of this equation predicts oscillatory and monotonic dispersal behaviors, which are observed in experimental populations of blowfly species.
RESUMO
A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. First-order drug kinetics and drug resistance are taken into account in a class of optimal control problems. The results show that the strategy corresponding to the maximum rate of drug injection is optimal for the Malthusian model of cell growth (which is a relatively good model for the initial phase of tumor growth). For more general models of cell growth, this strategy proved to be suboptimal under certain conditions.
Assuntos
Antineoplásicos/farmacologia , Antineoplásicos/farmacocinética , Neoplasias/tratamento farmacológico , Divisão Celular/efeitos dos fármacos , Resistência a Medicamentos , Humanos , Matemática , Modelos Biológicos , Neoplasias/metabolismo , Neoplasias/patologiaRESUMO
A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Drug resistance and toxicity conveyed through the level of normal cells are taken into account in a class of optimal control problems. Alternative treatments for the exponential tumor growth are set forth for cases where optimal treatments are not available.
Assuntos
Antineoplásicos/farmacologia , Neoplasias/tratamento farmacológico , Antineoplásicos/efeitos adversos , Antineoplásicos/farmacocinética , Morte Celular/efeitos dos fármacos , Divisão Celular/efeitos dos fármacos , Resistência a Medicamentos , Humanos , Matemática , Modelos Biológicos , Neoplasias/metabolismo , Neoplasias/patologiaRESUMO
A system of differential equations for the control of tumour cell growth in a cycle-nonspecific chemotherapy is presented. A rate-of-kill term of saturation type, drug resistance, and toxicity are taken into account in a class of optimal control problems. Some results are obtained for general tumour cell growth rates. A detailed analysis is presented for the Malthusian cell growth, which shows a variety of optimal treatments according to the values of the model parameters and initial tumour level.
Assuntos
Antineoplásicos/uso terapêutico , Resistência a Medicamentos , Matemática , Neoplasias/tratamento farmacológico , Neoplasias/patologia , Antineoplásicos/administração & dosagem , Antineoplásicos/toxicidade , Ciclo Celular , Divisão Celular , Humanos , Modelos TeóricosRESUMO
A system of differential equations for the control of the growth of certain populations by the use of chemical treatment is presented. Rather general growth rates and kill rates of drugs, as well as drug resistance, are considered. A class of optimal control problems with a performance criterion depending on a parameter is formulated and shown to admit the same basic optimal strategy. Applications to cycle nonspecific chemotherapy and control of the growth of bacterial populations in cellulose media in paper production plants are described.