Modeling West Nile Virus transmission in birds and humans: Advantages of using a cellular automata approach.

In Canada, the periodic circulation of West Nile Virus (WNV) is difficult to predict and, beyond climatic factors, appears to be related to the migratory movements of infected birds from the southern United States. This hypothesis has not yet been explored in a spatially distributed model. The main objective of this work was to develop a spatially explicit dynamic model for the transmission of WNV in Canada, that allows us to explore non-climate related hypotheses associated with WNV transmission. A Cellular Automata (CA) approach for multiple hosts (birds and humans) is used for a test region in eastern Ontario, Canada. The tool is designed to explore the role of host and vector spatial heterogeneity, host migration, and vector feeding preferences. We developed a spatialized compartmental SEIRDS-SEI model for WNV transmission with a study region divided into 4 km2 rectangular cells. We used 2010-2021 bird data from the eBird project and 2010-2019 mosquito data collected by Ontario Public Health to mimic bird and mosquito seasonal variation. We considered heterogeneous bird densities (high and low suitability areas) and homogeneous mosquito and human densities. In high suitability areas for birds, we identified 5 entry points for WNV-infected birds. We compared our simulations with pools of WNV-infected field collected mosquitoes. Simulations and sensitivity analyses were performed using MATLAB software. The results showed good correspondence between simulated and observed epidemics, supporting the validity of our model assumptions and calibration. Sensitivity analysis showed that a 5% increase or decrease in each parameter of our model except for the biting rate of bird by mosquito (c(B,M)) and mosquito natural mortality rate (dM), had a very limited effect on the total number of cases (newly infected birds and humans), prevalence peak, or date of occurrence. We demonstrate the utility of the CA approach for studying WNV transmission in a heterogeneous landscape with multiple hosts.

Temporal patterns in Ixodes ricinus microbial communities: an insight into tick-borne microbe interactions.

BACKGROUND: Ticks transmit pathogens of medical and veterinary importance and are an increasing threat to human and animal health. Assessing disease risk and developing new control strategies requires identifying members of the tick-borne microbiota as well as their temporal dynamics and interactions. METHODS: Using high-throughput sequencing, we studied the Ixodes ricinus microbiota and its temporal dynamics. 371 nymphs were monthly collected during three consecutive years in a peri-urban forest. After a Poisson lognormal model was adjusted to our data set, a principal component analysis, sparse network reconstruction, and differential analysis allowed us to assess seasonal and monthly variability of I. ricinus microbiota and interactions within this community. RESULTS: Around 75% of the detected sequences belonged to five genera known to be maternally inherited bacteria in arthropods and to potentially circulate in ticks: Candidatus Midichloria, Rickettsia, Spiroplasma, Arsenophonus and Wolbachia. The structure of the I. ricinus microbiota varied over time with interannual recurrence and seemed to be mainly driven by OTUs commonly found in the environment. Total network analysis revealed a majority of positive partial correlations. We identified strong relationships between OTUs belonging to Wolbachia and Arsenophonus, evidence for the presence of the parasitoid wasp Ixodiphagus hookeri in ticks. Other associations were observed between the tick symbiont Candidatus Midichloria and pathogens belonging to Rickettsia. Finally, more specific network analyses were performed on TBP-infected samples and suggested that the presence of pathogens belonging to the genera Borrelia, Anaplasma and Rickettsia may disrupt microbial interactions in I. ricinus. CONCLUSIONS: We identified the I. ricinus microbiota and documented marked shifts in tick microbiota dynamics over time. Statistically, we showed strong relationships between the presence of specific pathogens and the structure of the I. ricinus microbiota. We detected close links between some tick symbionts and the potential presence of either pathogenic Rickettsia or a parasitoid in ticks. These new findings pave the way for the development of new strategies for the control of ticks and tick-borne diseases. Video abstract.

Global formal live poultry and hatching egg trade network (2004-2016): description and association with poultry disease reporting and presence.

As international trade constitutes one of the main spread pathways of diseases, a better understanding of the trade behaviors of countries will help identify strengths and areas for improvement in the approach of national authorities to controlling poultry diseases globally. Using data reported to the United Nations Comtrade and the World Organisation for Animal Health (OIE) between 2004 and 2016 by 193 countries, we used a network analysis on trade data of poultry hatching eggs, live poultry of less than 185 g and live poultry of 185 g or more to determine that: 1) quantities traded between countries are substantial, and tend to increase (average increase of 800,000 poultry heads and 21,000 tons of hatching eggs each year equivalent to an increase by 2-fold in 17 yr); 2) the stability of the networks was low (a quarter to half of trade relationships maintained between 2 consecutive years) and the subnetworks favorable to the spread of diseases were in general consistent with regional clustering, trade exchanges being equally at intracontinental and intercontinental levels; 3) countries with highest number of partners were located in the same world regions for the 3 poultry networks - Americas and Europe for export (up to 107 partners) and Africa, Asia and Europe for import (up to 36 partners); 4) for live poultry, biggest exporting countries shared more poultry disease surveillance data, and reported more disease presence than others, which did not stop them from trading. Biggest importers reported less poultry disease surveillance data and reported more disease presence than others; and 5) the main structural and trend characteristics of the international trade networks were in general similar for the 3 networks. The information derived from this work underlines the importance of applying the preventive measures advocated by the OIE and will support countries to reduce the risk of introduction of pathogens causing poultry diseases.

Implication, clinical and biological impact of vector-borne haemopathogens in anaemic dogs in France: a prospective study.

OBJECTIVES: To prospectively describe the clinical and biological impact of vector-borne haemopathogens in anaemic dogs in France and occurrence of haemolysis. MATERIALS AND METHODS: This prospective descriptive cohort study includes 134 client-owned dogs that were anaemic on admission at the Veterinary Teaching Hospital of VetAgro Sup, Lyon, France. They underwent comprehensive screening with PCR to detect a panel of vector-borne haemopathogens, SNAP Leishmania and SNAP 4Dx Plus (IDEXX). RESULTS: Vector-borne haemopathogen-associated anaemia accounted for 17·2% (23/134) of anaemic cases. PCR for Babesia species, Mycoplasma species, Anaplasma platys or Ehrlichia canis and positive serology for Leishmania species, occurred in 11/23, 10/23, 2/23, 1/23 and 1/23 cases, respectively. Two dogs had positive PCR for both Babesia and Mycoplasma species. All dogs infected with Mycoplasma species alone had neoplastic disease. Vector-borne haemopathogens were the second most common cause of haemolysis (7/23, 30·4%). In the multivariable regression model, males were overrepresented ( OR : 2·82, P=0·03) and haemolysis ( OR : 3·31, P=0·01) was more frequent in dogs with vector-born haemopathogen-associated anaemia. CLINICAL SIGNIFICANCE: Vector-borne haemopathogens are a common cause of anaemia in this geographical region.

Prediction of Parturition Time in Queens using Radiography and Ultrasonography.

This study investigated the prediction of parturition in queens, as well as the effects of the queens' age and weight and the litter size on the accuracy of the prediction. A prospective study was performed in 24 purebred queens of 11 different breeds, all in normal body condition, using radiographic and ultrasonographic measurements of foetal femoral length (FL) and biparietal diameter (BPD) of fœtal skull that apply to different breeds. Pregnant queens with aborted or malformed foetuses were excluded. The examinations were performed up to three times during the second half of pregnancy; litter size was obtained with radiography, and FL and BPD measurements were taken of each foetus using both radiography and ultrasonography. The maximal FL and the transversal BPD were recorded for each foetus. Radiography showed the number of foetuses accurately but did not allow accurate prediction of time of parturition. However, ultrasonography did establish the best predictive model according to the data with the FL. This model corresponded to the formula Y = 37.864 - 0.193 × FL + 1.227 × W - 0.615 × LS - 0.832 × A using the FL (10(-1)  mm), litter size (LS, number of foetuses per queen) and maternal parameters (weight (W, kg) and age (A, years)). Time to parturition correlated positively with the queen's weight and negatively with her age (P < 0.01). The ultrasonographic FL associated with pregnancy and maternal factors appeared to be an accurate model to predict parturition.

Impact of climate change in the epidemiology of vector-borne diseases in domestic carnivores.

Vector-borne diseases are medically important in humans and animals but were long considered tropical and known to first affect production animals. This is no longer true and we can see today that they are common in domestic animals and that they are also present in temperate countries, especially in Europe. In recent years, an increase in the diagnosis of vector borne diseases among humans and animals has been observed, which may partly due to the development of diagnostic tools. Their study requires exchanges and collaborations between the many actors involved, especially since the epidemiology seems to be constantly evolving. The veterinary practitioner is the first one to notice the emergence of cases and to implement prevention measures. He also acts as a sentinel to alert epidemiologists. Many factors can explain the epidemiological changes, i.e. all human factors, such as the increase in commercial transportation, but also owners traveling with their pet during the holidays, the development of "outdoor" activities, the increase of individual housings with gardens; to these human factors must be added the ignorance of the risks, linked to animals in general and to wildlife in particular; then the environmental changes: forest fragmentation, establishment of parks; the increase of wild mammal populations (deer, carnivores, rodents, etc.); finally, climate changes. Climate change is a reality which may explain the increase of density of arthropod vectors, but also of their hosts, changes in periods of activity and variations in geographical distribution. The authors show the proof of the climate modifications and then explain how it has an impact in Europe on ticks, mosquitoes, sandflies and even fleas. They conclude on the practical consequences for veterinary practitioners, especially with the diagnosis of parasitic diseases or diseases in areas where they usually do not occur. However, not any epidemiological modification should be linked to climate change, since many other factors are involved and often even overriding.

Clinical signs, seasonal occurrence and causative agents of canine babesiosis in France: results of a multiregional study.

Canine babesiosis (or piroplasmosis) is an emerging tick-borne disease caused by intraerythrocytic protozoa of the genera Babesia and Theileria. In dogs, infection by these parasites usually induces a haemolytic syndrome that can be fatal when complicated. Canine babesiosis prevalence is high in France, with Babesia canis thought to be the main etiological agent of the disease. This article presents the results of a multiregional prospective longitudinal survey on canine babesiosis conducted in France from October 2006 to December 2007. A total of 836 cases were reported by veterinarians using a multiple choice questionnaire and blood samples from 70 dogs were analyzed using PCR-RFLP to identify species responsible for canine babesiosis cases across the country. The main clinical signs reported were lethargy (98%), anorexia (98%) and hyperthermia ≥ 39 °C (80%) followed by pale mucous membranes (54%), modification of urine aspect (45%) and splenomegaly (33%). The dog population at risk was mainly represented by young dogs living in rural areas. Twenty-five out of the 70 blood samples (36%) tested by diagnostic PCR were found to contain Babesia/Theileria genus-specific DNA and all had profiles similar to that of Babesia canis genomic DNA after restriction fragment length polymorphism analyses. The survey results provide a reference for further molecular studies to assess the species and vectors involved in the transmission of the disease in France and across the Mediterranean basin.

Comparative efficacy on dogs of a single topical treatment with fipronil/(S)-methoprene or weekly physiological hygiene shampoos against Ctenocephalides felis in a simulated flea-infested environment.

Flea infestations of pets continue to persist due to the lack of knowledge of flea biology and ecology. It is not unusual that pet owners believe regular hygiene, such as shampooing their dogs can replace regular insecticidal treatment. The objective of this study was to compare in a flea simulated environment, modelling exposure similar to that found in a home, that the use of regular physiological shampoo does not control fleas adequately when compared to a long acting topical formulation. Three groups of six dogs were formed: one untreated control group, one group treated monthly with the topical formulation of fipronil/(S)-methoprene, and a third group treated weekly with a hygiene shampoo. All dogs were infested with adult unfed Ctenocephalides felis fleas (200±5) on Days -28 and -21. Each animal's sleeping box was fitted with a plastic cup mounted to the inside roof of the box. The sleeping bench of each animal was covered with a carpet to accommodate flea development. The dogs were maintained in their kennels throughout the study. In order to maintain the environmental flea challenge, C. felis pupae (100±5) were placed in the plastic cup in each animal's sleeping box on Days -14, -7, 0, 7, 14, 21, 28, 35 and 42. The dogs were combed and fleas counted weekly on Days -1, 3, 10, 17, 24, 31, 38, 45, and 51. The fleas were placed immediately back on the dogs. On Day 60, fleas were counted and removed. Flea infestations in the untreated control group at each count averaged between 46.2 and 74.2 fleas throughout the study. The average number of fleas infesting dogs was significantly different (p<0.05) between the untreated and the two treatment groups and between the two treatment groups at all counts throughout the two months study (Days 3, 10, 17, 24, 31, 38, 45, 51 and 60). The efficacy was never below 99.1% in the fipronil/(S)-methoprene group, and efficacy in the shampoo group was never above 79.2%. Weekly shampooing in treatment group 3 was intentionally delayed after Day 42, to evaluate wether missing a weekly bath would affect the flea population. The Day 48 data indicate that forgetting or delaying a single weekly shampooing resulted in a clear increase in flea numbers and a significant decrease in efficacy from 68.2% to 34.8%. The fipronil(S)/methoprene treatment allowed a continuous control as demonstrated by the high efficacy against fleas, and also the number of flea-free dogs on seven of the nine weekly assessments, in spite of what was essentially a continuous flea challenge model.

Estimating spatial and temporal variations of the reproduction number for highly pathogenic avian influenza H5N1 epidemic in Thailand.

Since 2003, highly pathogenic avian influenza (HPAI) H5N1 virus has spread, causing a pandemic with serious economic consequences and public health implications. Quantitative estimates of the spread of HPAI H5N1 are needed to adapt control measures. This study aimed to estimate the variations of the reproduction number R in space and time for the HPAI H5N1 epidemic in Thailand. Transmission between sub-districts was analyzed using three different and complementary methods. Transmission of HPAI H5N1 was intense (R(t)>1) before October 2004, at which point the epidemic started to progressively fade out (R(t)<1). The spread was mainly local, with 75% of the putative distances of transmission less than 32km. The map of the mean standardized ratio of transmitting the infection (sr) showed sub-districts with a high risk of transmitting infection. Findings from this study can contribute to discussions regarding the efficacy of control measures and help target surveillance programs.

Comparative efficacy on dogs of a single topical treatment with the pioneer fipronil/(S)-methoprene and an oral treatment with spinosad against Ctenocephalides felis.

In the study reported here, the pioneer fipronil/(S)-methoprene topical product (Frontline® Plus, Merial Limited, Duluth, GA) was compared to the oral spinosad product (Comfortis® Elanco, Greenfield, IN) for efficacy against adult fleas and preventing egg production. The product presentations, doses and labelling were the one applicable in the USA. Using a standard protocol, 200 cat fleas of mixed sex were applied to dogs on Days 1, 7, 14, 21, 28, 35, and 42. Dogs were combed to remove fleas 24 hours post-infestation, the fleas were counted, collected, and then reapplied to each dog following completion of their respective count. At 48 hours post-infestation, comb counts were performed and fleas were removed. No fleas were collected from any dog in the fipronil/(S)-methoprene group at any 24 or 48 hours post-infestation assessment throughout the six weeks study, yielding a preventive efficacy of 100%. For the spinosad treatment, efficacy was 100% at 24 hours and 48 hours through Day 16, and thereafter declined. The results observed in the spinosad-treated dogs were highly variable between animals. At the 24 and 48 hours counts following the Day 21 infestation, only five of eight spinosad-treated dogs (62.5%) were flea-free. Following the Day  28 infestation, spinosad efficacy fell to 85% and 89%, for the 24 hours and 48 hours counts, and only two dogs (25%) were flea free, compared to 100% flea-free dogs in the fipronil/(S)-methoprene group. No fleas were collected from the fipronil/(S)-methoprene treated dogs throughout the entire study, therefore, no eggs were collected at any time from any dog in the group. However, in the spinosad group adult fleas were found on dogs starting on Day 21 and by Day 30, 42 eggs were collected from one dog that had 107 adult fleas counted at 48 hours. At Day 37 and Day 49, more than 100 eggs were collected from each dog in the spinosad-treated and control groups.

Relationships between fetal biometry, maternal factors and birth weight of purebred domestic cat kittens.

The goal of this study was to evaluate the relation between kittens' birth weights and biometrical factors from the kittens and the mother during pregnancy. Knowing fetal birth weight could help in detecting abnormalities before parturition. A Caesarean-section or a postnatal management plan could be scheduled. Consequently, the neonatal mortality rate should be decreased. We used ultrasonographic measurements of femur length (FL) or fetal biparietal diameter (BPD), pregnancies, and maternal factors to obtain a model of prediction. For this purpose, linear mixed-effects models were used because of random effects (several fetuses for one queen and a few paired measurements) and fixed effects (litter size, pregnancy rank, weight, wither height, and age of the queen). This study was performed in 24 purebred queens with normal pregnancies and normal body conditions. Queens were scanned in the second half of pregnancy, using a micro-convex probe. They gave birth to 140 healthy kittens whose mean birth weight was 104 g (ranged 65 to 165 g). No correlation between the birth weight and the age of the queen, as a maternal factor alone, was observed. But the birth weight was found to be inversely proportional to the pregnancy rank and the litter size. Moreover, birth weight increased when the weight and wither height of queen increased. BPD and FL increased linearly during pregnancy so a model was used to estimate mean birth weight. Using this model, we found a correlation between mean birth weights and an association of parameters: maternal factors (wither height and age), and litter size.

Monthly district level risk of dengue occurrences in Sakon Nakhon Province, Thailand.

The paper deals with the incidence of the Dengue Virus Infection (DVI) in the 18 districts of Sakon Nakhon Province, Thailand, from January 2005 to December 2007. Using a statistical and autoregressive analysis to smooth incidence data, we have constructed yearly and monthly district level maps of the DVI distribution. It is found that the DVI incidence is very correlated with weather conditions and higher occurrences are observed in the three most populated districts Wanon Niwat, Sawang Daen Din and Mueang Sakon Nakhon, and the virus transmission period spans from mid-summer to mid-rainy seasons (from April to August). Employing a Generalized Linear Model (GLM), we found that the DVI incidences were related with current meteorological (monthly minimum temperature, past 2-month cumulated rainfall) and socio-economical (population of 0-4years old, per capita number of public small water wells, and proportion of villages with primary schools) covariates. And using the GLM under the climate change conditions (A1B scenario of IPCC), we found that the higher risk of DVI spreads from the three most populated districts to less populated ones, and the period of virus transmission increases from 5 to 9months to include part of winter, summer and rainy seasons (from March to November) during which 6%, 61% and 33% of districts will be at low, medium and high risk of DVI occurrences, respectively.

Risk factors for West Nile virus seropositivity of equids in Guadeloupe.

In Guadeloupe, West Nile virus (WNV) activity was first observed in equids in 2002, and a high seroprevalence was found in 2003. The objective of our study was to determine individual and environmental factors associated with the risk of WNV seropositivity during 2002-2003. Fieldwork was conducted to retrospectively determine the location of equids at the time of virus circulation and to collect information regarding environmental and individual variables. Sera were collected from 369 equids out of an estimated total population of less than 500. Thirty-four environmental and individual variables were investigated. Equids had a higher risk (p<0.001) for WNV seropositivity if they lived within the proximity "distance less than 1.5km" of marshes or swamp forests "a large freshwater formation behind mangroves" or if they remained outside after dusk. Equids living within the proximity of ouassous shrimp (Macrobrachium rosenbergii) basins or sugar cane fields had a lower risk (p<0.001) for WNV seropositivity. These results confirm that WNV circulation is more likely in the humid coastal areas of Guadeloupe. The identification of risk factors is useful for predicting future emergence sites of WNV in the archipelago and other Neotropical islands, and to better target sentinel surveillance in the region.

Genetic and environmental risk indicators in canine non-Hodgkin's lymphomas: breed associations and geographic distribution of 608 cases diagnosed throughout France over 1 year.

BACKGROUND: The etiology of non-Hodgkin's lymphomas (NHL) is multifactorial. Environmental and genetic factors are frequently incriminated both in humans and dogs. OBJECTIVES: Our purpose was to study the geographic distribution of canine NHL (CNHL) in France and to evaluate genetic and environmental influences. ANIMALS: Six hundred and eight cases of CNHL, diagnosed throughout France over 1 year, were collected from 7 Veterinary Histopathologic Laboratories. METHODS: Retrospective study. Breeds affected by lymphomas were compared with the national population and associations between breed and immunophenotype were studied. The distribution of CNHL and canine T-cell NHL per 100,000 dogs per department was compared with the distribution of waste incinerators, polluted sites, and radioactive waste. RESULTS: The breeds significantly overrepresented among lymphoma cases were Boxer, Setter, and Cocker Spaniel (P < .001). There was a significant association between Boxer and T-cell NHL (P < .001), and between German Shepherd and Rottweiler and B-cell NHL (P < .01). The geographic distribution of CNHL and canine T-cell NHL indicated significant heterogeneity. Significant association between distributions of CNHL and waste incinerators (rho= 0.25, P < .05), polluted sites (rho= 0.36, P < .001), and radioactive waste (rho= 0.51, P < .001) was found. CONCLUSIONS AND CLINICAL IMPORTANCE: Influence of genetics in the development of CNHL was supported by the existence of an association between breed and immunophenotype. Waste incinerators, polluted sites, and radioactive waste could just be considered as risk indicators of CNHL, but not as risk factors. Case-control studies around critical sites are necessary to confirm the implication of those environmental factors in the development of CNHL.

Modelling and determination of the transmission contact rate for contagious bovine pleuropneumonia.

Contagious bovine pleuropneumonia (CBPP) is a cattle respiratory disease that represents one of the major threats to cattle health and production in sub-Saharan Africa. The transmission contact rate of CBPP plays a key role in the spreading dynamics of the disease. We have developed an approach based on the combination of a SEIR model describing the spread of CBPP with the dynamic of seroconversion to determine the transmission contact rate for CBPP. This method has been subsequently applied to serological diagnostic data obtained from an experimental vaccine trial. As a result, we find that the transmission contact rates for subclinical, clinical and chronic infective states are respectively, 0.084/N, 0.45 and 0.14/N per animal per day, where N is the herd population size, and the basic reproductive number corresponding to this trial (N=28) is R0=27.

A mathematical model of the population dynamics of Heterakis gallinarum in turkeys (Meleagridis gallopavo).

Heterakis gallinarum is a relatively nonpathogenic organism, but it is important as the transport host for the pathogenic protozoan Histomonas meleagridis. A mathematical model was developed to describe the population dynamics of Heterakis gallinarum in a turkey flock to study its kinetics in a number of hosts. The model includes quantitative (parasite burden) and qualitative (number of hosts without mature parasite) descriptions of these dynamics. To understand the role of Heterakis as a transport host, the various elements that delay the beginning of development of the parasite population (e.g., necessary delay of larval stage, the probability of having a male and female in the same host) were taken into account. From published data, the negative binomial distribution parameter k = 0.24, which described the aggregated distribution of the Heterakis among the hosts, was calculated. The sensibility study showed that when the k parameter decreased (i.e., when the population was more aggregated), infestation increased quantitatively (mean parasite burden increased) but not qualitatively (the number of host without mature parasite increased). The model demonstrated that the population dynamics of Heterakis takes time; for instance, with an aggregated population of Heterakis at d 90, the host is mainly free of adult parasite. These results may be used in the future to test the role of Heterakis in the spread of Histomonas.

Use of a mathematical model to study the dynamics of Ctenocephalides felis populations in the home environment and the impact of various control measures.

The biology of fleas has been studied by a number of authors, as has the impact of various types of control measures. However, there are no mathematical models simulating the dynamics of a population of Ctenocephalides felis felis fleas on their host (the cat) and in their close environment (apartment). The model presented in this paper allows for integration of the numerous biological and behavioural parameters of the parasites and their hosts and for the variation of these same parameters. The various types of control measures can be programmed so that their impact over time can be studied. The model confirms the key role played by adult fleas, or emerged fleas contained in the cocoon. Only regular applications of persistent insecticides to the host animal will enable control of the parasite population. A combination of these insecticides with an IGR (Insect Growth Regulator) will accelerate decontamination of the home environment and see the disappearance of the parasites altogether if they are not reintroduced. The association of additional measures such as vacuum cleaning will accelerate the process of decontamination but will have no impact if carried out in isolation. One-off treatment with insecticide will not enable a reduction in the parasite population, even if carried out frequently. Use of insecticides on the home environment premises alone does not appear to be an adequate means of control. The present model can be used to test various integrated control measures which take into account different factors such as the number of host animals, the frequency of movement outdoors, the impact of the seasons.

Use of a mathematical model to study the control measures of the cattle tick Boophilus microplus population in New Caledonia.

Boophilus microplus is a common cattle tick of great economic importance in various tropical and subtropical countries like New Caledonia. The proposed model describes the population dynamics of female Boophilus microplus in the absence of resistant ticks. It is a system of six difference equations which can be mathematically analyzed. The analysis of the system shows the great importance of the eigenvalue denoted by lambda1. The population of ticks increases if lambda1 < 1 and decreases if lambda1 > 1. The lambda1 eigenvalue depends, in particular, on the parasitic surviving rate and encounter rate between the larvae and the cows. The treatments decrease the parasitic surviving rate as the agronomic measures decrease the encounter rate. This model permits to quantify the conditions of treatments (or of the efficacy of a vaccine) and of agronomic measures by which the populations are controlled. It shows that the different treatment rhythms and the presence or not of the wild or domestic refuges plays a major role on the dynamics of tick population.

A two-patch model of Gambian sleeping sickness: application to vector control strategies in a village and plantations.

A compartmental model is described for the spread of Gambian sleeping sickness in a spatially heterogeneous environment in which vector and human populations migrate between two "patches": the village and the plantations. The number of equilibrium points depends on two "summary parameters": gr the proportion removed among human infections, and R0, the basic reproduction number. The origin is stable for R0 < 1 and unstable for R0 > 1. Control strategies are assessed by studying the mix of vector control between the two patches that bring R0 below 1. The results demonstrate the importance of vector control in the plantations. For example if 20 percent of flies are in the village and the blood meal rate in the village is 10 percent, then a 20 percent added vector mortality in the village must be combined with a 9 percent added mortality in the plantations in order to bring R0 below 1. The results are quite insensitive to the blood meal rate in the village. Optimal strategies (that minimize the total number of flies trapped in both patches) are briefly discussed.