A mathematical model of vector-borne infectious diseases is presented, which takes into account the local interactions between reservoirs and vectors, as well as the transmission from vectors to dilution hosts. In the model, vectors possess the ability to keep the virus within their own population through vertical transmission. The existence and the stability of disease free and endemic equilibria, together with the existence of backward bifurcation, are discussed

Antonella Lupica

Annunziata Palumbo

Frontal view of the third from the north upper portal mosaic, depicting the Resurrection; Studies by the excavator, Forlati, indicate that S Marco was a centrally planned, Greek-cross building from the start. The present building was begun ca. 1063 under Doge Domenico Contarini (reg 1043-1071), who wished it to reflect the increased power and wealth of Venice. He preserved the earlier foundations and reused some of the outside walls and brickwork of the earlier building. It was consecrated in 1094. S Marco is built of brick with a marble facing. It is centrally planned, on a Greek cross, with an east-west axis of 76.5 m (including the later narthex), and has five hemispherical domes on pendentives, one at the centre and one on each of the four arms. The internal height of the central dome is 28.5 m. Venetian chroniclers state that Byzantine architects were summoned, again basing the church on the Holy Apostles (remodelled in the 9th century) at Constantinople. The origins of the architect have been much debated, but the building was probably a fusion of different regional ideas. The detached campanile (now 98.6 m high) seems to have been created from an ancient look-out tower, probably in the second half of the 12th century. The campanile collapsed in 1902 and was faithfully rebuilt in 1912. Source: Grove Art Online; http://www.oxfordartonline.com/ (accessed 7/17/2008

unknown

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Saint Mark's Basilica

View of reliefs; Studies by the excavator, Forlati, indicate that S Marco was a centrally planned, Greek-cross building from the start. The present building was begun ca. 1063 under Doge Domenico Contarini (reg 1043-1071), who wished it to reflect the increased power and wealth of Venice. He preserved the earlier foundations and reused some of the outside walls and brickwork of the earlier building. It was consecrated in 1094. S Marco is built of brick with a marble facing. It is centrally planned, on a Greek cross, with an east-west axis of 76.5 m (including the later narthex), and has five hemispherical domes on pendentives, one at the centre and one on each of the four arms. The internal height of the central dome is 28.5 m. Venetian chroniclers state that Byzantine architects were summoned, again basing the church on the Holy Apostles (remodelled in the 9th century) at Constantinople. The origins of the architect have been much debated, but the building was probably a fusion of different regional ideas. The detached campanile (now 98.6 m high) seems to have been created from an ancient look-out tower, probably in the second half of the 12th century. The campanile collapsed in 1902 and was faithfully rebuilt in 1912. Source: Grove Art Online; http://www.oxfordartonline.com/ (accessed 7/17/2008

View looking up at the apse; Studies by the excavator, Forlati, indicate that S Marco was a centrally planned, Greek-cross building from the start. The present building was begun ca. 1063 under Doge Domenico Contarini (reg 1043-1071), who wished it to reflect the increased power and wealth of Venice. He preserved the earlier foundations and reused some of the outside walls and brickwork of the earlier building. It was consecrated in 1094. S Marco is built of brick with a marble facing. It is centrally planned, on a Greek cross, with an east-west axis of 76.5 m (including the later narthex), and has five hemispherical domes on pendentives, one at the centre and one on each of the four arms. The internal height of the central dome is 28.5 m. Venetian chroniclers state that Byzantine architects were summoned, again basing the church on the Holy Apostles (remodelled in the 9th century) at Constantinople. The origins of the architect have been much debated, but the building was probably a fusion of different regional ideas. The detached campanile (now 98.6 m high) seems to have been created from an ancient look-out tower, probably in the second half of the 12th century. The campanile collapsed in 1902 and was faithfully rebuilt in 1912. Source: Grove Art Online; http://www.oxfordartonline.com/ (accessed 7/17/2008

unknown (Italian)

View of the south facade, depicting the entry to the baptistery, with the so-called "Pilaster of Acre" on the right; Studies by the excavator, Forlati, indicate that S Marco was a centrally planned, Greek-cross building from the start. The present building was begun ca. 1063 under Doge Domenico Contarini (reg 1043-1071), who wished it to reflect the increased power and wealth of Venice. He preserved the earlier foundations and reused some of the outside walls and brickwork of the earlier building. It was consecrated in 1094. S Marco is built of brick with a marble facing. It is centrally planned, on a Greek cross, with an east-west axis of 76.5 m (including the later narthex), and has five hemispherical domes on pendentives, one at the centre and one on each of the four arms. The internal height of the central dome is 28.5 m. Venetian chroniclers state that Byzantine architects were summoned, again basing the church on the Holy Apostles (remodelled in the 9th century) at Constantinople. The origins of the architect have been much debated, but the building was probably a fusion of different regional ideas. The detached campanile (now 98.6 m high) seems to have been created from an ancient look-out tower, probably in the second half of the 12th century. The campanile collapsed in 1902 and was faithfully rebuilt in 1912. Source: Grove Art Online; http://www.oxfordartonline.com/ (accessed 7/17/2008

Central portal, detail of columns at the right of the portal; Studies by the excavator, Forlati, indicate that S Marco was a centrally planned, Greek-cross building from the start. The present building was begun ca. 1063 under Doge Domenico Contarini (reg 1043-1071), who wished it to reflect the increased power and wealth of Venice. He preserved the earlier foundations and reused some of the outside walls and brickwork of the earlier building. It was consecrated in 1094. S Marco is built of brick with a marble facing. It is centrally planned, on a Greek cross, with an east-west axis of 76.5 m (including the later narthex), and has five hemispherical domes on pendentives, one at the centre and one on each of the four arms. The internal height of the central dome is 28.5 m. Venetian chroniclers state that Byzantine architects were summoned, again basing the church on the Holy Apostles (remodelled in the 9th century) at Constantinople. The origins of the architect have been much debated, but the building was probably a fusion of different regional ideas. The detached campanile (now 98.6 m high) seems to have been created from an ancient look-out tower, probably in the second half of the 12th century. The campanile collapsed in 1902 and was faithfully rebuilt in 1912. Source: Grove Art Online; http://www.oxfordartonline.com/ (accessed 7/17/2008

North portal, frontal view; Studies by the excavator, Forlati, indicate that S Marco was a centrally planned, Greek-cross building from the start. The present building was begun ca. 1063 under Doge Domenico Contarini (reg 1043-1071), who wished it to reflect the increased power and wealth of Venice. He preserved the earlier foundations and reused some of the outside walls and brickwork of the earlier building. It was consecrated in 1094. S Marco is built of brick with a marble facing. It is centrally planned, on a Greek cross, with an east-west axis of 76.5 m (including the later narthex), and has five hemispherical domes on pendentives, one at the centre and one on each of the four arms. The internal height of the central dome is 28.5 m. Venetian chroniclers state that Byzantine architects were summoned, again basing the church on the Holy Apostles (remodelled in the 9th century) at Constantinople. The origins of the architect have been much debated, but the building was probably a fusion of different regional ideas. The detached campanile (now 98.6 m high) seems to have been created from an ancient look-out tower, probably in the second half of the 12th century. The campanile collapsed in 1902 and was faithfully rebuilt in 1912. Source: Grove Art Online; http://www.oxfordartonline.com/ (accessed 7/17/2008

Horses of St. Mark, general view, depicting location above central portal; Studies by the excavator, Forlati, indicate that S Marco was a centrally planned, Greek-cross building from the start. The present building was begun ca. 1063 under Doge Domenico Contarini (reg 1043-1071), who wished it to reflect the increased power and wealth of Venice. He preserved the earlier foundations and reused some of the outside walls and brickwork of the earlier building. It was consecrated in 1094. S Marco is built of brick with a marble facing. It is centrally planned, on a Greek cross, with an east-west axis of 76.5 m (including the later narthex), and has five hemispherical domes on pendentives, one at the centre and one on each of the four arms. The internal height of the central dome is 28.5 m. Venetian chroniclers state that Byzantine architects were summoned, again basing the church on the Holy Apostles (remodelled in the 9th century) at Constantinople. The origins of the architect have been much debated, but the building was probably a fusion of different regional ideas. The detached campanile (now 98.6 m high) seems to have been created from an ancient look-out tower, probably in the second half of the 12th century. The campanile collapsed in 1902 and was faithfully rebuilt in 1912. Source: Grove Art Online; http://www.oxfordartonline.com/ (accessed 7/17/2008

Detail of the Onion Dome surmounting the central Ascension Dome; Studies by the excavator, Forlati, indicate that S Marco was a centrally planned, Greek-cross building from the start. The present building was begun ca. 1063 under Doge Domenico Contarini (reg 1043-1071), who wished it to reflect the increased power and wealth of Venice. He preserved the earlier foundations and reused some of the outside walls and brickwork of the earlier building. It was consecrated in 1094. S Marco is built of brick with a marble facing. It is centrally planned, on a Greek cross, with an east-west axis of 76.5 m (including the later narthex), and has five hemispherical domes on pendentives, one at the centre and one on each of the four arms. The internal height of the central dome is 28.5 m. Venetian chroniclers state that Byzantine architects were summoned, again basing the church on the Holy Apostles (remodelled in the 9th century) at Constantinople. The origins of the architect have been much debated, but the building was probably a fusion of different regional ideas. The detached campanile (now 98.6 m high) seems to have been created from an ancient look-out tower, probably in the second half of the 12th century. The campanile collapsed in 1902 and was faithfully rebuilt in 1912. Source: Grove Art Online; http://www.oxfordartonline.com/ (accessed 7/17/2008

View of the north facade; Studies by the excavator, Forlati, indicate that S Marco was a centrally planned, Greek-cross building from the start. The present building was begun ca. 1063 under Doge Domenico Contarini (reg 1043-1071), who wished it to reflect the increased power and wealth of Venice. He preserved the earlier foundations and reused some of the outside walls and brickwork of the earlier building. It was consecrated in 1094. S Marco is built of brick with a marble facing. It is centrally planned, on a Greek cross, with an east-west axis of 76.5 m (including the later narthex), and has five hemispherical domes on pendentives, one at the centre and one on each of the four arms. The internal height of the central dome is 28.5 m. Venetian chroniclers state that Byzantine architects were summoned, again basing the church on the Holy Apostles (remodelled in the 9th century) at Constantinople. The origins of the architect have been much debated, but the building was probably a fusion of different regional ideas. The detached campanile (now 98.6 m high) seems to have been created from an ancient look-out tower, probably in the second half of the 12th century. The campanile collapsed in 1902 and was faithfully rebuilt in 1912. Source: Grove Art Online; http://www.oxfordartonline.com/ (accessed 7/17/2008

Horses of St. Mark, rear view; Studies by the excavator, Forlati, indicate that S Marco was a centrally planned, Greek-cross building from the start. The present building was begun ca. 1063 under Doge Domenico Contarini (reg 1043-1071), who wished it to reflect the increased power and wealth of Venice. He preserved the earlier foundations and reused some of the outside walls and brickwork of the earlier building. It was consecrated in 1094. S Marco is built of brick with a marble facing. It is centrally planned, on a Greek cross, with an east-west axis of 76.5 m (including the later narthex), and has five hemispherical domes on pendentives, one at the centre and one on each of the four arms. The internal height of the central dome is 28.5 m. Venetian chroniclers state that Byzantine architects were summoned, again basing the church on the Holy Apostles (remodelled in the 9th century) at Constantinople. The origins of the architect have been much debated, but the building was probably a fusion of different regional ideas. The detached campanile (now 98.6 m high) seems to have been created from an ancient look-out tower, probably in the second half of the 12th century. The campanile collapsed in 1902 and was faithfully rebuilt in 1912. Source: Grove Art Online; http://www.oxfordartonline.com/ (accessed 7/17/2008

A mathematical model of vertically transmitted vector diseases

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