Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model

Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution function of the returns. We derive this distribution function using for C(K) a Black-Scholes (BS) expression with volatility in the form of a volatility smile. We show that this approach based on a volatility smile leads to relative minima for the distribution function ("bad" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring "adiabatic" conditions on the volatility smile

Contribution of land use to rodent flea load distribution in the plague endemic area of Lushoto District, Tanzania

Fleas associated with different rodent species are considered as the major vectors of bubonic plague, which is still rampant in different parts of the world. The objective of this study was to investigate the contribution of land use to rodent flea load distribution at fine scale in the plague endemic area of north-eastern Tanzania. Data was collected in three case areas namely, Shume, Lukozi and Mwangoi, differing in plague incidence levels. Data collection was carried out during both wet and dry seasons of 2012. Analysis of Variance and Boosted Regression Tree (BRT) statistical methods were used to clarify the relationships between fleas and specific land use characteristics. There was a significant variation (P ≤ 0.05) of flea indices in different land use types. Fallow and natural forest had higher flea indices whereas plantation forest mono-crop and mixed annual crops had the lowest flea indices among the aggregated land use types. The influence of individual land use types on flea indices was variable with fallow having a positive effect and land tillage showing a negative effect. The results also demonstrated a seasonal effect, part of which can be attributed to different land use practices such as application of pesticides, or the presence of grass strips around fields. These findings suggest that land use factors have a major influence on rodent flea abundance which can be taken as a proxy for plague infection risk. The results further point to the need for a comprehensive package that includes land tillage and crop type considerations on one hand and the associated human activities on the other, in planning and implementation of plague control interventions

Contribution of land use to rodent flea load distribution in the plague endemic area of Lushoto District, Tanzania

Fleas associated with different rodent species are considered as the major vectors of bubonic plague, which is still rampant in different parts of the world. The objective of this study was to investigate the contribution of land use to rodent flea load distribution at fine scale in the plague endemic area of north-eastern Tanzania. Data was collected in three case areas namely, Shume, Lukozi and Mwangoi, differing in plague incidence levels. Data collection was carried out during both wet and dry seasons of 2012. Analysis of Variance and Boosted Regression Tree (BRT) statistical methods were used to clarify the relationships between fleas and specific land use characteristics. There was a significant variation (P ≤ 0.05) of flea indices in different land use types. Fallow and natural forest had higher flea indices whereas plantation forest mono-crop and mixed annual crops had the lowest flea indices among the aggregated land use types. The influence of individual land use types on flea indices was variable with fallow having a positive effect and land tillage showing a negative effect. The results also demonstrated a seasonal effect, part of which can be attributed to different land use practices such as application of pesticides, or the presence of grass strips around fields. These findings suggest that land use factors have a major influence on rodent flea abundance which can be taken as a proxy for plague infection risk. The results further point to the need for a comprehensive package that includes land tillage and crop type considerations on one hand and the associated human activities on the other, in planning and implementation of plague control interventions

Human activity spaces and plague risks in three contrasting landscapes in Lushoto District, Tanzania

Tanzania Journal of Health Research Volume 16, Number 3, July 2014Since 1980 plague has been a human threat in the Western Usambara Mountains in Tanzania. However, the spatial-temporal pattern of plague occurrence remains poorly understood. The main objective of this study was to gain understanding of human activity patterns in relation to spatial distribution of fleas in Lushoto District. Data were collected in three landscapes differing in plague incidence. Field survey coupled with Geographic Information System (GIS) and physical sample collections were used to collect data in wet (April to June 2012) and dry (August to October 2012) seasons. Data analysis was done using GIS, one-way ANOVA and nonparametric statistical tools. The degree of spatial co- occurrence of potential disease vectors (fleas) and humans in Lushoto focus differs significantly (p ≤ 0.05) among the selected landscapes, and in both seasons. This trend gives a coarse indication of the possible association of the plague outbreaks and the human frequencies of contacting environments with fleas. The study suggests that plague surveillance and control programmes at landscape scale should consider the existence of plague vector contagion risk gradient from high to low incidence landscapes due to human presence and intensity of activities

Small mammals distribution and diversity in a plague endemic area in West Usambara Mountains, Tanzania

Small mammals play a role in plague transmission as hosts in all plague endemic areas. Information on distribution and diversity of small mammals is therefore important for plague surveillance and control in such areas. The objective of this study was to investigate small mammals’ diversity and their distribution in plague endemic area in the West Usambara Mountains in north-eastern Tanzania. Landsat images and field surveys were used to select trapping locations in different landscapes. Three landscapes with different habitats were selected for trapping of small mammals. Three types of trap were used in order to maximise the number of species captured. In total, 188 animals and thirteen species were captured in 4,905 trap nights. Praomys delectorum and Mastomys natalensis both reported as plague hosts comprised 50% of all the animals trapped. Trap success increased with altitude. Species diversity was higher in plantation forest followed by shrub, compared to other habitats, regardless of landscape type. It would therefore seem that chances of plague transmission from small mammals to humans are much higher under shrub, natural and plantation forest habitats

Land use determinants of small mammal abundance and distribution in a plague endemic area of Lushoto District, Tanzania

Small mammals are considered to be involved in the transmission cycle of bubonic plague, still occurring in different parts of the world, including the Lushoto District in Tanzania. The objective of this study was to determine the relationship between land use types and practices and small mammal abundance and distribution. A field survey was used to collect data in three landscapes differing in plague incidences. Data collection was done both in the wet season (April-June 2012) and dry season (August- October 2012). Analysis of variance and Boosted Regression Trees (BRT) modelling technique were used to establish the relationship between land use and small mammal abundance and distribution. Significant variations (p ≤ 0.05) of small mammal abundance among land use types were identified. Plantation forest with farming, natural forest and fallow had higher populations of small mammals than the other aggregated land use types. The influence of individual land use types on small mammal abundance level showed that, in both dry and wet seasons, miraba and fallow tended to favour small mammals’ habitation whereas land tillage practices had the opposite effect. In addition, during the wet season crop types such as potato and maize appeared to positively influence the distribution and abundance of small mammals which was attributed to both shelter and food availability. Based on the findings from this study it is recommended that future efforts to predict and map spatial and temporal human plague infection risk at fine scale should consider the role played by land use and associated human activities on small mammal abundance and distribution

Integrating land cover and terrain characteristics to explain plague risks in Western Usambara Mountains, Tanzania: a geospatial approach

Literature suggests that higher resolution remote sensing data integrated in Geographic Information System (GIS) can provide greater possibility to refine the analysis of land cover and terrain characteristics for explanation of abundance and distribution of plague hosts and vectors and hence of health risk hazards to humans. These technologies are not widely used in East Africa for studies on diseases including plague. The objective of this study was to refine the analysis of single and combined land cover and terrain characteristics in order to gain an insight into localized plague infection risks in the West Usambara Mountains in north-eastern Tanzania. The study used a geospatial approach to assess the influence of land cover and terrain factors on the abundance and spatial distribution of plague hosts (small mammals) and plague vectors (fleas). It considered different levels of scale and resolution. Boosted Regression Tree (BRT) statistical method was used to clarify the relationships between land cover and terrain variables with small mammals and fleas. Results indicate that elevation positively influenced the presence of small mammals. The presence of fleas was clearly influenced by land management features such as miraba. Medium to high resolution remotely sensed data integrated in a GIS have been found to be quite useful in this type of analysis. These findings contribute to efforts on plague surveillance and awareness creation among communities on the probable risks associated with various landscape factors during epidemics

Human activity spaces and plague risks in three contrasting landscapes in Lushoto District, Tanzania

Tanzania Journal of Health Research Volume 16, Number 3, July 2014Since 1980 plague has been a human threat in the Western Usambara Mountains in Tanzania. However, the spatial-temporal pattern of plague occurrence remains poorly understood. The main objective of this study was to gain understanding of human activity patterns in relation to spatial distribution of fleas in Lushoto District. Data were collected in three landscapes differing in plague incidence. Field survey coupled with Geographic Information System (GIS) and physical sample collections were used to collect data in wet (April to June 2012) and dry (August to October 2012) seasons. Data analysis was done using GIS, one-way ANOVA and nonparametric statistical tools. The degree of spatial co- occurrence of potential disease vectors (fleas) and humans in Lushoto focus differs significantly (p ≤ 0.05) among the selected landscapes, and in both seasons. This trend gives a coarse indication of the possible association of the plague outbreaks and the human frequencies of contacting environments with fleas. The study suggests that plague surveillance and control programmes at landscape scale should consider the existence of plague vector contagion risk gradient from high to low incidence landscapes due to human presence and intensity of activities

Land use determinants of small mammal abundance and distribution in a plague endemic area of Lushoto District, Tanzania

Small mammals are considered to be involved in the transmission cycle of bubonic plague, still occurring in different parts of the world, including the Lushoto District in Tanzania. The objective of this study was to determine the relationship between land use types and practices and small mammal abundance and distribution. A field survey was used to collect data in three landscapes differing in plague incidences. Data collection was done both in the wet season (April-June 2012) and dry season (August- October 2012). Analysis of variance and Boosted Regression Trees (BRT) modelling technique were used to establish the relationship between land use and small mammal abundance and distribution. Significant variations (p ≤ 0.05) of small mammal abundance among land use types were identified. Plantation forest with farming, natural forest and fallow had higher populations of small mammals than the other aggregated land use types. The influence of individual land use types on small mammal abundance level showed that, in both dry and wet seasons, miraba and fallow tended to favour small mammals’ habitation whereas land tillage practices had the opposite effect. In addition, during the wet season crop types such as potato and maize appeared to positively influence the distribution and abundance of small mammals which was attributed to both shelter and food availability. Based on the findings from this study it is recommended that future efforts to predict and map spatial and temporal human plague infection risk at fine scale should consider the role played by land use and associated human activities on small mammal abundance and distribution

Vegetation habitats and small mammals in a plague endemic area in Western Usambara Mountains, Tanzania

Human plague still exists in different parts of the world, including some landscapes in north- eastern Tanzania. Wherever the hotspot of plague, small mammals seem to play a key role as host. The objective of this study was to investigate the relationship between vegetation habitats types and small mammals in a plague endemic area of Lushoto District in Tanzania. A combination of field survey and Landsat images was used to identify the vegetation habitats. Small mammals were trapped in the mapped vegetation units, and identified. In total, six main types of vegetation habitats were investigated. A total of 13 small mammal species, potentially related to plague were trapped. Results show that annual cultivated crops habitat accounted for 80% of Mastomys natalensis while natural forest accounted for 60% of Praomys delectorum. These findings have shed new light on the diversity of rodents in different habitats of natural and semi-natural vegetations, and agricultural crops in the study area, which is an important intermediate step in unravelling the complex human plague system