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A hierarchical network approach for modeling Rift Valley fever epidemics with applications in North America.

Xue L, Cohnstaedt LW, Scott HM, Scoglio C - PLoS ONE (2013)

Bottom Line: Spatial effects and climate factors are also addressed in the model.A surprising trend is fewer initial infectious organisms result in a longer delay before a larger and more prolonged outbreak.Cattle movement between farms is a large driver of virus expansion, thus quarantines can be efficient mitigation strategy to prevent further geographic spread.

View Article: PubMed Central - PubMed

Affiliation: Kansas State Epicenter, Department of Electrical and Computer Engineering, Kansas State University, Manhattan, Kansas, United States of America.

ABSTRACT
Rift Valley fever is a vector-borne zoonotic disease which causes high morbidity and mortality in livestock. In the event Rift Valley fever virus is introduced to the United States or other non-endemic areas, understanding the potential patterns of spread and the areas at risk based on disease vectors and hosts will be vital for developing mitigation strategies. Presented here is a general network-based mathematical model of Rift Valley fever. Given a lack of empirical data on disease vector species and their vector competence, this discrete time epidemic model uses stochastic parameters following several PERT distributions to model the dynamic interactions between hosts and likely North American mosquito vectors in dispersed geographic areas. Spatial effects and climate factors are also addressed in the model. The model is applied to a large directed asymmetric network of 3,621 nodes based on actual farms to examine a hypothetical introduction to some counties of Texas, an important ranching area in the United States of America. The nodes of the networks represent livestock farms, livestock markets, and feedlots, and the links represent cattle movements and mosquito diffusion between different nodes. Cattle and mosquito (Aedes and Culex) populations are treated with different contact networks to assess virus propagation. Rift Valley fever virus spread is assessed under various initial infection conditions (infected mosquito eggs, adults or cattle). A surprising trend is fewer initial infectious organisms result in a longer delay before a larger and more prolonged outbreak. The delay is likely caused by a lack of herd immunity while the infection expands geographically before becoming an epidemic involving many dispersed farms and animals almost simultaneously. Cattle movement between farms is a large driver of virus expansion, thus quarantines can be efficient mitigation strategy to prevent further geographic spread.

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The relationship between egg laying rates, egg development rates of mosquitoes and climate factors.(A) The egg laying rates of Aedes and Culex mosquitoes with moisture [35]. (B) The egg development rate of Culex mosquitoes with temperature [35]. (C) The egg laying rates of Aedes and Culex mosquitoes in the nine counties in the south of Texas from January,  to October, . (D) The egg development rate of Culex mosquitoes in one region of Texas from January,  to October, . (E) The egg development rate of Aedes mosquitoes with temperature. (F) The egg development rate of Aedes mosquitoes in one region of Texas from January,  to October, .
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pone-0062049-g002: The relationship between egg laying rates, egg development rates of mosquitoes and climate factors.(A) The egg laying rates of Aedes and Culex mosquitoes with moisture [35]. (B) The egg development rate of Culex mosquitoes with temperature [35]. (C) The egg laying rates of Aedes and Culex mosquitoes in the nine counties in the south of Texas from January, to October, . (D) The egg development rate of Culex mosquitoes in one region of Texas from January, to October, . (E) The egg development rate of Aedes mosquitoes with temperature. (F) The egg development rate of Aedes mosquitoes in one region of Texas from January, to October, .

Mentions: The egg laying rates of Aedes and Culex mosquitoes changing with moisture conditions as indicated in Equation (21) [35] are shown in Fig. 2A. The egg development rate of Aedes mosquitoes varying with temperature in Equation [36] and that of Culex mosquitoes in Equation are in Fig. 2E and Fig. 2B, respectively. The parameters for egg laying rates of Aedes mosquitoes and Culex mosquitoes, and parameters for egg development rate of Culex mosquitoes are derived from data concerning West Nile virus in in the Northern U.S. [35], and the parameters for the egg development rate of Aedes mosquitoes is derived using the model for Aedes aegypti [36], which are the best models currently available. More precise parameters can be adopted, as they become available. The egg laying rates of Aedes and Culex mosquitoes, egg development rate of Culex mosquitoes, and egg development rate of Aedes mosquitoes computed with the climate data for the region where cattle farm and markets located in the study area of Texas from January, to October, , are shown in Fig. 2C, Fig. 2D, and Fig. 2F, respectively. If the temperature is too low, the eggs will not develop into larvae and then adult mosquitoes. If the temperature is too high, the lifespan of the mosquitoes is shortened and the development rate decreases. Moisture index is the difference between precipitation and evaporation as shown in Equation (22). A lower moisture index correlates to fewer adult mosquitoes because low moisture index represents a combination of low precipitation and high evaporation. For some days, the missing precipitation data from January, to December, [37] are assumed to be zero. The evaporation data are calculated using Equation (23) [38]. The parameters in Equations (21) through (25) are listed in Table 3. Although humans move between nodes, they do not transmit virus between nodes and the number of humans in each node (i.e., farm) is assumed to be fewer than .


A hierarchical network approach for modeling Rift Valley fever epidemics with applications in North America.

Xue L, Cohnstaedt LW, Scott HM, Scoglio C - PLoS ONE (2013)

The relationship between egg laying rates, egg development rates of mosquitoes and climate factors.(A) The egg laying rates of Aedes and Culex mosquitoes with moisture [35]. (B) The egg development rate of Culex mosquitoes with temperature [35]. (C) The egg laying rates of Aedes and Culex mosquitoes in the nine counties in the south of Texas from January,  to October, . (D) The egg development rate of Culex mosquitoes in one region of Texas from January,  to October, . (E) The egg development rate of Aedes mosquitoes with temperature. (F) The egg development rate of Aedes mosquitoes in one region of Texas from January,  to October, .
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3646918&req=5

pone-0062049-g002: The relationship between egg laying rates, egg development rates of mosquitoes and climate factors.(A) The egg laying rates of Aedes and Culex mosquitoes with moisture [35]. (B) The egg development rate of Culex mosquitoes with temperature [35]. (C) The egg laying rates of Aedes and Culex mosquitoes in the nine counties in the south of Texas from January, to October, . (D) The egg development rate of Culex mosquitoes in one region of Texas from January, to October, . (E) The egg development rate of Aedes mosquitoes with temperature. (F) The egg development rate of Aedes mosquitoes in one region of Texas from January, to October, .
Mentions: The egg laying rates of Aedes and Culex mosquitoes changing with moisture conditions as indicated in Equation (21) [35] are shown in Fig. 2A. The egg development rate of Aedes mosquitoes varying with temperature in Equation [36] and that of Culex mosquitoes in Equation are in Fig. 2E and Fig. 2B, respectively. The parameters for egg laying rates of Aedes mosquitoes and Culex mosquitoes, and parameters for egg development rate of Culex mosquitoes are derived from data concerning West Nile virus in in the Northern U.S. [35], and the parameters for the egg development rate of Aedes mosquitoes is derived using the model for Aedes aegypti [36], which are the best models currently available. More precise parameters can be adopted, as they become available. The egg laying rates of Aedes and Culex mosquitoes, egg development rate of Culex mosquitoes, and egg development rate of Aedes mosquitoes computed with the climate data for the region where cattle farm and markets located in the study area of Texas from January, to October, , are shown in Fig. 2C, Fig. 2D, and Fig. 2F, respectively. If the temperature is too low, the eggs will not develop into larvae and then adult mosquitoes. If the temperature is too high, the lifespan of the mosquitoes is shortened and the development rate decreases. Moisture index is the difference between precipitation and evaporation as shown in Equation (22). A lower moisture index correlates to fewer adult mosquitoes because low moisture index represents a combination of low precipitation and high evaporation. For some days, the missing precipitation data from January, to December, [37] are assumed to be zero. The evaporation data are calculated using Equation (23) [38]. The parameters in Equations (21) through (25) are listed in Table 3. Although humans move between nodes, they do not transmit virus between nodes and the number of humans in each node (i.e., farm) is assumed to be fewer than .

Bottom Line: Spatial effects and climate factors are also addressed in the model.A surprising trend is fewer initial infectious organisms result in a longer delay before a larger and more prolonged outbreak.Cattle movement between farms is a large driver of virus expansion, thus quarantines can be efficient mitigation strategy to prevent further geographic spread.

View Article: PubMed Central - PubMed

Affiliation: Kansas State Epicenter, Department of Electrical and Computer Engineering, Kansas State University, Manhattan, Kansas, United States of America.

ABSTRACT
Rift Valley fever is a vector-borne zoonotic disease which causes high morbidity and mortality in livestock. In the event Rift Valley fever virus is introduced to the United States or other non-endemic areas, understanding the potential patterns of spread and the areas at risk based on disease vectors and hosts will be vital for developing mitigation strategies. Presented here is a general network-based mathematical model of Rift Valley fever. Given a lack of empirical data on disease vector species and their vector competence, this discrete time epidemic model uses stochastic parameters following several PERT distributions to model the dynamic interactions between hosts and likely North American mosquito vectors in dispersed geographic areas. Spatial effects and climate factors are also addressed in the model. The model is applied to a large directed asymmetric network of 3,621 nodes based on actual farms to examine a hypothetical introduction to some counties of Texas, an important ranching area in the United States of America. The nodes of the networks represent livestock farms, livestock markets, and feedlots, and the links represent cattle movements and mosquito diffusion between different nodes. Cattle and mosquito (Aedes and Culex) populations are treated with different contact networks to assess virus propagation. Rift Valley fever virus spread is assessed under various initial infection conditions (infected mosquito eggs, adults or cattle). A surprising trend is fewer initial infectious organisms result in a longer delay before a larger and more prolonged outbreak. The delay is likely caused by a lack of herd immunity while the infection expands geographically before becoming an epidemic involving many dispersed farms and animals almost simultaneously. Cattle movement between farms is a large driver of virus expansion, thus quarantines can be efficient mitigation strategy to prevent further geographic spread.

Show MeSH
Related in: MedlinePlus