Matthieu Lesnoff

Sensitivity analysis in periodic matrix models: A postscript to Caswell and Trevisan

Periodic matrix population models are a useful approach t@ modelling cyclic variations in demographic rates. Caswell and Trevisan [1] introduced the perturbation analysis (sensitivities and elasticities) @f the per-cycle population growth rate for such models. Although powerful, their method can be time-consuming when the dimension of the matrices is large @r when cycles are composed of many phases. We present a more efficient method, based @n a very simple matrix product. We compared the two methods for matrices of different sizes. We observed a reduction in calculation time on the order of 24% with the new method for a set @f 26 within-year Leslie matrices of size 287 x 287. The time saving may become particularly significant when sensitivities are used in Monte Carlo or bootstrap simulations.

Use of Akaike information criteria for model selection and inference. An application to assess prevention of gastrointestinal parasitism and respiratory mortality of Guinean goats in Kolda, Senegal.

A field experiment was carried out in Kolda (southern Senegal) from July 1986 to July 1988. Its goals were to: (1) describe the patterns of mortality of female Guinean goats by age, season and year; (2) assess preventive measures against respiratory diseases and gastrointestinal parasitism in reducing mortality; and (3) estimate the overall impact of these measures on survival to 1 year of age. Preventive measures for respiratory disease included vaccination against peste des petits ruminants (PPR) and pneumonic pasteurellosis (Pasteurella multocida types A and D). Control of gastrointestinal parasites was by deworming does with morantel (7.5mg kg(-1), three times during the rainy season). The effects of vaccines and deworming were tested in a randomised factorial field experiment with villages being the experimental units. A total of 19 villages, 113 goat herds and 1,458 goats were included in the study. Generalised linear models of survival for five cohorts of goats (defined by five different birth seasons) used a binomial assumption for the response distribution and a complementary log-log link. Explanatory variables included age, season, year, vaccination, deworming and their interactions. A complex a priori model was built on the basis of previous epidemiological knowledge; a purposely selected set of simpler models was compared to this full model by the Akaike information criterion (AIC) and derived statistics. Inference on 1-year survival and treatment effects accounted for model-selection uncertainty. It was carried out with a bootstrap procedure and used information from the whole set of selected models. Large variations in mortality by year and season were observed but no regular seasonal pattern was apparent. Mortality probabilities of kids in dewormed groups decreased quickly after birth, but remained elevated up to 9 months of age in the non-dewormed groups. Deworming lowered the risk of mortality. Vaccination alone was not protective (except during an observed outbreak of PPR).

A steady-state approach of benefit–cost analysis with a periodic Leslie-matrix model: Presentation and application to the evaluation of a sheep-diseases preventive scheme in Kolda, Senegal

A seasonal population-dynamics matrix model (periodic Leslie-matrix model) was developed to model short production cycles and high seasonal variations occurring in demographic rates and offtake patterns for small ruminants. The year was split into 24- and 15-day phases. Population-size changes were modelled by the recurrence equation x(j+1)=B(j)x(j), where j was the 15-day phase, x an age-class population size vector and B a fecundity-, mortality-, offtake- and intake-rate matrix. Given an initial vector x(1), annual dynamics were described by x(25)=B(24)...B(1)x(1)=Ax(1), where A was the annual projection matrix.A steady-state hypothesis was used to estimate offtake gains and financial returns from a trial of pasteurellosis vaccination and anthelminthic drench in traditionally managed sheep flocks in Senegal, from July 1987 to June 1988. Nineteen villages and 76 herds were involved in the experiment. Villages were randomly allocated to one of the four treatment combinations in a factorial design, and subsequent demographic rates and net offtake patterns were measured. In the trial, vaccination had a negative effect on offtakes among females. No vaccination effect was observed for males. A positive effect of deworming was found for both sexes. From the trial data, our model calculated that the overall ratio of offtakes (i.e. number of animals) for dewormed over undrenched sheep was 1.2 (95% confidence interval: 1.1, 1.4). The deworming financial benefit-cost ratio was 3.7 (1.9, 5.4).

A simple model for simulating immunity rate dynamics in a tropical free-range poultry population after avian influenza vaccination

In developing countries, vaccination against highly pathogenic avian influenza subtype H5N1 (HPAI) in free-range poultry flocks is usually implemented as periodic campaigns and newborn chicks are generally not vaccinated by farmers between vaccination passes. The demographic population turnover leads to a continuous decrease in the population immunity rate (PIR) over time. We present a simple Leslie matrix model for estimating population turnover and PIR dynamics in a hypothetical small-size vaccinated free-range poultry population. Four different vaccination scenarios were identified assuming necessary procedures to achieve immunity. The results indicate that high levels of population immunity are difficult to sustain. Assuming an animal immunity response of 80% after vaccination and a constant population size, PIR 4 months after vaccination was 30% in all the scenarios. Predictions averaged over time showed mean PIR between 36% and 48%, which is below the population immunity thresholds for eradication approximated from R0 estimates.

A metapopulation model for the spread and persistence of contagious bovine pleuropneumonia (CBPP) in african sedentary mixed crop-livestock systems

Contagious bovine pleuropneumonia (CBPP) is endemic in several developing countries. Our objective is to evaluate the regional CBPP spread and persistence in a mixed crop-livestock system in Africa. A stochastic compartmental model in metapopulation is used, in which between-herd animal movements and the within-herd infection dynamics are explicitly represented. Hundred herds of varying size are modelled, each sending animals to n other herds (network degree). Animals are susceptible, latent, infectious, chronic carrier or resistant. The role of chronic carriers in CBPP spread being still debated, several chronic periods and infectiousness are tested. A sensitivity analysis is performed to evaluate the influence on model outputs of these parameters and of pathogen virulence, between-herd movement rate, network degree, and calves recruitment. Model outputs are the probability that individual- and group-level reproductive numbers R(0) and R(*) are above one, the metapopulation infection duration, the probability of CBPP endemicity (when CBPP persists over 5 years), and the epidemic size in infected herds and infected animals. The most influential parameters are related to chronic carriers (infectiousness and chronic period), pathogen virulence, and recruitment rate. When assuming no CBPP re-introduction in the region, endemicity is only probable if chronic carriers are assumed infectious for at least 1 year and to shed the pathogen in not too low an amount. It becomes highly probable when assuming high pathogen virulence and high recruitment rate.

Graphical approaches to support the analysis of linear-multilevel models of lamb pre-weaning growth in Kolda (Senegal).

Linear-multilevel models (LMM) are mixed-effects models in which several levels of grouping may be specified (village, herd, animal, ellipsis). This study highlighted the usefulness of graphical methods in their analysis through: (1) the choice of the fixed and random effects and their structure, (2) the assessment of goodness-of-fit and (3) distributional assumptions for random effects and residuals. An LMM was developed to study the effect of ewe deworming with morantel on lamb pre-weaning growth in a field experiment involving 182 lambs in 45 herds and 10 villages in Kolda, Senegal. Growth was described as a quadratic polynomial of age. Other covariates were sex, litter-size and treatment. The choice of fixed and random effects relied on three graphs: (1) a trellis display of mean live-weight vs. age, to select main effects and interactions (fixed effects); (2) a trellis display of individual growth curves, to decide which growth-curve terms should be included as random effects and (3) a scatter plot of parameters of lamb-specific regressions (live-weight vs. quadratic polynomial of age) to choose the random-effects covariance structure.Age, litter-size, agexlitter-size, litter-sizextreatment and agexlitter-sizextreatment were selected graphically as fixed effects and were significant (p<0.05) in subsequent statistical models. The selection of random-effect structures was guided by graphical assessment and comparison of the Akaikes information criterion for different models. The final random-effects selected included no random effect at the village level but intercept, age and squared-age at the herd and lamb levels. The structure of the random-effects variance-covariance matrices were blocked-diagonal at the herd level and unstructured at the lamb level. An order-1 autoregressive structure was retained to account for serial correlations of residuals. Smaller residual variance at 90 days than at younger ages was modeled with a dummy variable taking a value of 1 at 90 days and 0 elsewhere.Ewe-deworming with morantel during the rainy season lead to higher lamb live-weights (probably related to a better ewe-nutrition and -health status). A positive correlation was demonstrated between early weight and growth rate at the population level (with important lamb and herd-level random deviations). The persistence of this correlation at older ages should be checked to determine whether early weights are good predictors of mature weights and ewe-reproductive lifetime performance.

Performance evaluation of two serological tests for contagious bovine pleuropneumonia (CBPP) detection in an enzootic area using a Bayesian framework

A Bayesian approach, allowing for conditional dependence between two tests was used to estimate without gold standard the sensitivities of complement fixation test (CFT) and competitive enzyme-linked immunosorbent assay test (cELISA) and the serological prevalence of CBPP in a cattle population of the Central Delta of the Niger River in Mali, where CBPP is enzootic and the true prevalence and animals serological state were unknown. A significant difference (P = 0.99) was observed between the sensitivities of the two tests, estimated at 73.7% (95% probability interval [PI], 63.4–82.7) for cELISA and 42.3% (95% PI, 33.3–53.7) for CFT. Individual-level serological prevalence in the study population was estimated at 14.1% (95% PI, 10.8–16.9). Our results indicate that in enzootic areas, cELISA performs better in terms of sensitivity than CFT. However, negative conditional sensitivity dependence between the two tests was detected, implying that to achieve maximum sensitivity, the two tests should be applied in parallel.

Time-delay dynamics for contagious bovine pleuropneumonia.

Modelling of contagious disease usually employs compartmental SEIR-like models where the waiting times in respective compartments are exponentially distributed. In this paper, we are interested in investigating how the distributions of sojourn times in infective compartments affect the dynamics and persistence of the contagious bovine pleuropneumonia, a chronic respiratory disease of cattle. Two kinds of extreme distributions of the sojourn times are considered: a Dirac delta-function and truncated Gaussian function leading to a model with (non-constant) delay and the classical exponential distribution that stands for a model without delay. Expressions of the basic reproductive numbers are derived and dynamical behaviours are discussed for the three models. It is found that the spreading of disease exhibits wave-like oscillations for the time-delay dynamics. In contrast, the disease appears to last longer when the spreading is described by the classical dynamics without delay. Subsequently, the time-delay dynamics turns out to be more appropriate for the description of an experimental epidemic of CBPP.

Uncertainty analysis of the productivity of cattle populations in tropical drylands.

This article presents an uncertainty analysis of the productivity of cattle herds in traditional farming systems of West and Central African drylands. The study focused on productivity rates in animal numbers (RN) and meat weights (RW) estimated from a herd growth model, which were compared with FAOSTAT-based estimates. The uncertainty analysis contained the following two steps: uncertainty propagation and a global sensitivity analysis. The analysis was based on a state-of-the-art of the current knowledge and a set of available data on the herd performances. The calculations used Monte Carlo simulations to estimate the 95% confidence intervals (CI) of RN and RW and the standardized regression coefficients method to estimate the contribution of the input variables to the outputs variances. The mean rate RN was estimated to 0.127 animal/animal-year with a 95% CI of (0.091, 0.163) and the mean rate RW to 11.7 kg/animal-year with a 95% CI of (8.8, 14.7), corresponding to relative variation around the mean of about ± 29% and ± 25%, respectively. The input variables that contributed most to the variance of RN (almost 76% of the output variance) were the calving rate, the adult female mortality rate and the female proportion in the population (determined by the pattern of the male offtake in the herds). The input variables that contributed most to the variance of RW were the same as those for RN plus the adult live weights. The CI ranges that were estimated in this article indicate that productivity rates based on literature data or expert estimations of the herd performances should be considered with caution. Research efforts based on gold-standard herd monitoring protocols accounting for temporal and spatial variations should be undertaken in future to decrease the knowledge gaps on the input variables that contribute most to these ranges.

Ex-ante assessment of different vaccination-based control schedules against the peste des petits ruminants virus in sub-Saharan Africa

Background Peste des petits ruminants (PPR) is a highly contagious and widespread viral infection of small ruminants (goats and sheep), causing heavy economic losses in many developing countries. Therefore, its progressive control and global eradication by 2030 was defined as a priority by international organizations addressing animal health. The control phase of the global strategy is based on mass vaccination of small ruminant populations in endemic regions or countries. It is estimated that a 70% post-vaccination immunity rate (PVIR) is needed in a given epidemiological unit to prevent PPR virus spread. However, implementing mass vaccination is difficult and costly in smallholder farming systems with scattered livestock and limited facilities. Regarding this, controlling PPR is a special challenge in sub-Saharan Africa. In this study, we focused on this region to assess the effect of several variables of PVIR in two contrasted smallholder farming systems. Methods Using a seasonal matrix population model of PVIR, we estimated its decay in goats reared in sub-humid areas, and sheep reared in semi-arid areas, over a 4-year vaccination program. Assuming immunologically naive and PPR-free epidemiological unit, we assessed the ability of different vaccination scenarios to reach the 70% PVIR throughout the program. The tested scenarios differed in i) their overall schedule, ii) their delivery month and iii) their vaccination coverage. Results In sheep reared in semi-arid areas, the vaccination month did affect the PVIR decay though it did not in goats in humid regions. In both cases, our study highlighted i) the importance of targeting the whole eligible population at least during the two first years of the vaccination program and ii) the importance of reaching a vaccination coverage as high as 80% of this population. This study confirmed the relevance of the vaccination schedules recommended by international organizations.