<p>We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold parameter R0 is identified which governs the spread of diseases, and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 &lt / 1. This is the case of a disease-free&nbsp / state, with no infection in the population. Otherwise the disease may become endemic if the basic reproductive number R0 is bigger than unity. Furthermore, stability analysis for both endemic&nbsp / and disease-free steady states are investigated and we also give some numerical simulations. The second part of this dissertation deals with optimal vaccination strategy in epidemiology. We&nbsp / use optimal control technique on vaccination to minimize the impact of the disease. Hereby we mean minimizing the spread of the disease in the population, while also minimizing the effort on&nbsp / vaccination roll-out. We do this optimization for the cases of SIR and SEIR models, and show how optimal strategies can be obtained which minimize the damage caused by the infectious&nbsp / disease. Finally, we describe the numerical simulations using the fourth-order Runge-Kutta method.&nbsp / These are the most useful references: [G. Zaman, Y.H Kang, II. H. Jung. BioSystems 93,&nbsp / (2008), 240 &minus / 249], [K. Hattaf, N. Yousfi. The Journal of Advanced Studies in Biology, Vol. 1(8), (2008), 383 &minus / 390.], [Lenhart, J.T. Workman. Optimal Control and Applied to Biological Models.&nbsp / Chapman and Hall/CRC, (2007).], [P. Van den Driessche, J. Watmough. Math. Biosci., 7,&nbsp / (2005)], and [J. Wu, G. R&uml / ost. Mathematical Biosciences and Engineering, Vol 5(2), (2008), 389 &minus / 391].</p>

<p>We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold parameter R0 is identified which governs the spread of diseases, and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 &lt / 1. This is the case of a disease-free&nbsp / state, with no infection in the population. Otherwise the disease may become endemic if the basic reproductive number R0 is bigger than unity. Furthermore, stability analysis for both endemic&nbsp / and disease-free steady states are investigated and we also give some numerical simulations. The second part of this dissertation deals with optimal vaccination strategy in epidemiology. We&nbsp / use optimal control technique on vaccination to minimize the impact of the disease. Hereby we mean minimizing the spread of the disease in the population, while also minimizing the effort on&nbsp / vaccination roll-out. We do this optimization for the cases of SIR and SEIR models, and show how optimal strategies can be obtained which minimize the damage caused by the infectious&nbsp / disease. Finally, we describe the numerical simulations using the fourth-order Runge-Kutta method.&nbsp / These are the most useful references: [G. Zaman, Y.H Kang, II. H. Jung. BioSystems 93,&nbsp / (2008), 240 &minus / 249], [K. Hattaf, N. Yousfi. The Journal of Advanced Studies in Biology, Vol. 1(8), (2008), 383 &minus / 390.], [Lenhart, J.T. Workman. Optimal Control and Applied to Biological Models.&nbsp / Chapman and Hall/CRC, (2007).], [P. Van den Driessche, J. Watmough. Math. Biosci., 7,&nbsp / (2005)], and [J. Wu, G. R&uml / ost. Mathematical Biosciences and Engineering, Vol 5(2), (2008), 389 &minus / 391].</p>

>Magister Scientiae - MSc / We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold parameter R0 is identified which governs the spread of diseases, and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 < 1. This is the case of a disease-free state, with no infection in the population. Otherwise the disease may become endemic if the basic reproductive number R0 is bigger than unity. Furthermore, stability analysis for both endemic and disease-free steady states are investigated and we also give some numerical simulations. The second part of this dissertation deals with optimal vaccination strategy in epidemiology. We use optimal control technique on vaccination to minimize the impact of the disease. Hereby we mean minimizing the spread of the disease in the population, while also minimizing the effort on vaccination roll-out. We do this optimization for the cases of SIR and SEIR models, and show how optimal strategies can be obtained which minimize the damage caused by the infectious disease. Finally, we describe the numerical simulations using the fourth-order Runge-Kutta method.

Reliable estimates of species abundance, distribution, and population trajectories are critical in conservation and management. However, for many tropical species that information is missing. We conducted Sharp-shinned Hawk (SSHA) searches during the breeding seasons of 2013, 2014, and 2016 in eight montane forest reserves and their adjacent private lands of Puerto Rico. Further, we developed a maximum entropy model (MaxEnt) of the SSHA’s potential distribution using the following environmental variables: aspect, canopy closure, elevation, rainfall, slope, and terrain roughness. Elevation accounted for 89.8% of model fit, predicting the greatest probability of occurrence (> 60%) at elevations above 900 m. The model estimated 0.6% Puerto Rico (56.1 km2) has the greatest probability of occurrence. We developed a periodic population matrix model to describe influence of early life stages on population growth of the Red-tailed Hawk (RTHA) in eastern Puerto Rico. Our results suggest that the RTHA population has an average annual population increase of 5%, with rates differing between highlands (λh = 1.05) and 27% lowlands (λl = 1.27). Adult survival was the most important population growth parameter, with more effect in highlands (elasticity = 0.86) than in lowlands (elasticity = 0.53). Sensitivity of λ to changes in nestling survival was greater than for other life-stages (sensitivity lowlands = 0.46, sensitivity highlands = 0.48). I developed an open population N-mixture model to estimate abundance, availability, and detection probability of RTHA in the Luquillo Mountains and western Cordillera Central. The abundance estimates were 0.05 RTHA/ha, with an availability of (ϕ) = ~1 RTHA/per survey point and a detection probability (r) = ~0.25. In Luquillo Mountains, abundance was positively influenced by slope and elevation. In the western Cordillera Central, abundance of RTHA was constant across elevation, slope, and canopy closure. Detection probability decreased with increasing slope and wind conditions and showed a gradual small negative decrease with slope with reduced winds conditions. My findings are a contribution to our knowledge to how population traits and ecological constraints imposed by insular environments are influencing distribution, abundance, and population dynamics of raptors to propose management or conservation schemes.

Drug development is time consuming, expensive with high failure rates. It takes 10-15 years for a drug to go from discovery to approval, while the mean cost of developing a drug is $1.5 billions dollars. Pharmacometric models (PM) play a pivotal role in knowledge driven drug development and these models require validation prior to application. The purpose of the current study was to evaluate the posterior predictive check (PPC) and the bootstrap as population model validation tools. PPC was evaluated to determine, if it was able to distinguish between population pharmacokinetic (PPK) models that were developed/estimated from influence data versus models that were not derived/estimated from influence data. Bootstrap was examined to see if there was a correspondence between the root mean squared prediction errors (RMSPE) for serum concentrations when estimated by external prediction methods versus when estimated by the standard bootstrap. In the case of PPC, C last , C first -C last and C mid values from initial data sets were compared to corresponding posterior distributions. In the case of no influence data for C last , C first -C last and C mid on average 76%, 30% and 52% of the values from the posterior distributions were below the initial C last , C first -C last and C mid on average 93%, 13% and 67% of the values from the posterior distributions were below the initial C last , C first -C last and C mid respectively. PPC was able to classify models from influence versus no influence data. In the case of bootstrap when the original model was used to predict into the external data the WRMSPE for drug 1, drug 2, drug 3, drug 4 and simulated data set was 10.40 mg/L, 20.36 mg/L, 0.72 mg/L, 15.27 mg/L and 14.24 mg/L respectively. From the bootstrap the improved WRMSPE for drug 1 drug 2, drug 3, drug 4 and simulated data set was 9.35 mg/L, 19.85 mg/L, 0.50 mg/L, 14.44 mg/L and 13.98mg/L respectively. The bootstrap provided estimates of WRMSPE that corresponded to the external validation methods. From the results obtained, it was concluded that both the PPC and the Bootstrap were demonstrated to have value as validation tools.

Nesta tese estudamos os efeitos da desordem espacial e temporal na transição de fase entre a sobrevivência e extinção de populações biológicas. Na primeira parte estudamos um modelo epidemiológico com quatro estados. Apesar deste modelo não conter desordem, concluímos que seu comportamento crítico é o mesmo do processo de contato com desordem (espacial) quenched. Na segunda parte estudamos o movimento Browniano fracionário refletido, onde vimos que a combinação dos efeitos do ruído com correlações de longo alcance e a parede refletora cria uma singularidade em lei de potência na densidade de probabilidade da posição do caminhante. Por fim, estudamos a equação logística com desordem temporal através do mapeamento no movimento Browniano fracionário refletido. Neste último estudo vimos como as correlações de longo alcance mudam o comportamento crítico deste sistema. / We have studied the effects of spatial and temporal disorder at the phase transition between survival and extinction of biological populations. In the first part we studied a four states biological population model. Despite having no disorder, we have seen that its critical behavior is the same of the contact process with (spatial) quenched disorder. In the second part, we studied the reflected fractional Brownian motion, where the interplay between the correlated noise and the reflecting wall results in a power-law singularity in the probability density of the position of the walker. Finally, we deduced the critical properties of the logistic equation with temporal disorder by mapping it onto the reflected fractional Brownian motion. This mapping allow us to understand how long-range correlations change the critical behavior of this system.

Eastern Sand Darter (Ammocrypta pellucida) is listed as Threatened under the Canadian Species at Risk Act. Canadian populations are declining primarily due to the siltation of sandy depositional areas, the preferred habitat of the species. Little other relevant biological information is available for most Canadian populations and only limited information is available for populations in the United States. To supplement the paucity of information, this study collected biological information on A. pellucida during field surveys in 2006- 2007 from 10 sites located around the Big Bend Conservation Area in the lower Thames River, Ontario, Canada. Collected data were used to estimate critical life history traits including: longevity, fecundity, clutch size and number, growth, survival, age-at-first-maturity and cohort age structure. Longevity was 3+ years, with age-at-first-maturity being 1+ for both sexes. A minimum of 2 clutches, were laid per year with an average clutch size of 71 eggs. Average density within in the study area was 0.36 ± 0.11 A. pellucida/m². Quantitative comparison of lower Thames River biological information with a more southerly A. pellucida population in the Little Muskingum River, Ohio, demonstrated little latitudinal variation between the populations. Data comparison suggests that localized environmental factors are affecting biological characteristics, in particular water temperature that may be controlled by differences in riparian cover and/or groundwater input. Field derived life history information was used to create a Leslie matrix model which was used for population viability analysis. Perturbation analyses of reproductive scenarios involving changes in clutch numbers and size and age-at-first maturity found large variations in the finite rate of population growth. Elasticity analyses further indicated that 0+ survival and 1+ fertility were the limiting life history parameters. Thus allowing fish to survive until first reproduction would have the largest overall impact on improving population viability. Inclusion of environmental stochasticity in the model facilitated estimation of extinction probabilities in the range of 0.13 to 0.21 within 100 years. Based on the above, it is recommended that management activities for protection and restoration of A. pellucida focus on habitat protection of nursery and spawning areas.

Eastern Sand Darter (Ammocrypta pellucida) is listed as Threatened under the Canadian Species at Risk Act. Canadian populations are declining primarily due to the siltation of sandy depositional areas, the preferred habitat of the species. Little other relevant biological information is available for most Canadian populations and only limited information is available for populations in the United States. To supplement the paucity of information, this study collected biological information on A. pellucida during field surveys in 2006- 2007 from 10 sites located around the Big Bend Conservation Area in the lower Thames River, Ontario, Canada. Collected data were used to estimate critical life history traits including: longevity, fecundity, clutch size and number, growth, survival, age-at-first-maturity and cohort age structure. Longevity was 3+ years, with age-at-first-maturity being 1+ for both sexes. A minimum of 2 clutches, were laid per year with an average clutch size of 71 eggs. Average density within in the study area was 0.36 ± 0.11 A. pellucida/m². Quantitative comparison of lower Thames River biological information with a more southerly A. pellucida population in the Little Muskingum River, Ohio, demonstrated little latitudinal variation between the populations. Data comparison suggests that localized environmental factors are affecting biological characteristics, in particular water temperature that may be controlled by differences in riparian cover and/or groundwater input. Field derived life history information was used to create a Leslie matrix model which was used for population viability analysis. Perturbation analyses of reproductive scenarios involving changes in clutch numbers and size and age-at-first maturity found large variations in the finite rate of population growth. Elasticity analyses further indicated that 0+ survival and 1+ fertility were the limiting life history parameters. Thus allowing fish to survive until first reproduction would have the largest overall impact on improving population viability. Inclusion of environmental stochasticity in the model facilitated estimation of extinction probabilities in the range of 0.13 to 0.21 within 100 years. Based on the above, it is recommended that management activities for protection and restoration of A. pellucida focus on habitat protection of nursery and spawning areas.

Mettre en place des mesures de protection efficaces contre la dégradation et la fragmentation de l'habitat d'une espèce nécessite d'être capable de comprendre l'impact de l'environnement sur sa dynamique de population ainsi que sa sensibilité à la perte de connectivité entre les populations. Obtenir ces informations est déjà un défi en soi, qui se complique encore pour les espèces trop sensibles au dérangement pour être suivies de manière classique. Lors de ce travail, nous avons étudié la dynamique et la génétique des populations d'une chauve-souris forestière qui a subi un très fort déclin dans le nord de l'Europe, le Petit rhinolophe (Rhinolophus hipposideros), à l'aide de méthodes non-invasives (comptages, génétique non-invasive).Nos résultats ont montré que le climat et le paysage autour des colonies de maternités influence la taille et la dynamique des populations du Petit rhinolophe. Nous avons également confirmé un impact direct du paysage sur la survie des juvéniles. Enfin, nous avons observé que la diversité génétique des populations pouvait être fortement diminuée par leurs histoires démographiques et par un manque de connectivité entre les populations. Ces résultats ont des implications directes pour la conservation du Petit rhinolophe mais aussi pour le développement des analyses intégrant des données de génétique non-invasive pour la biologie de la conservation. / Efficient conservation management against habitat degradation and fragmentation of a species requires understanding how the environment impacts its population dynamics and the species’ sensitivity to connectivity loss. Acquiring sufficient knowledge about these processes is challenging for any species, and is even more complicated for species too sensitive to be studied with classical methods. During this work, we studied the population dynamics and genetics of a woodland specialized bat who has undergone a serious decline in the north of Europe, the lesser horseshoe bat (Rhinolophus hipposideros), with non-invasive methods (counts, non-invasive genetics).Our results shown that climate and landscape around maternity colonies explain population size variations and dynamics of the lesser horseshoe bat. We also confirmed a direct impact of landscape on juvenile survival. We finally observed that genetic diversity could be strongly decreased by population history and a lack of connectivity between populations. Our results have direct implications for the lesser horseshoe bat conservation but also for the development of analyses integrating non-invasive genetic data in conservation biology.

Cette thèse étudie l’influence de la diversité des tactiques d’histoire de vie sur la dynamique des populations de deux salmonidés à migration partielle: le saumon Atlantique, Salmo salar et la truite commune, Salmo trutta. Ces deux espèces ont de fortes valeurs écologique et économique, mais les rôles respectifs des individus résidents et migrateurs sur la dynamique et la résilience des populations à des changements environnementaux demeurent méconnus. Nous avons abordé ces questions par des approches démographiques, génétiques et de modélisation. Nous avons démontré que la détermination de la tactique d’histoire de vie est en partie plastique et permet aux individus juvéniles de migrer en réponse à un changement de l’environnement. De plus, cette thèse démontre que la diversité des tactiques permet aux populations à migration partielle de bénéficier d’un changement favorable de l’environnement et de réduire l’effet d’un changement défavorable sur la dynamique de populationCes deux processus pourraient expliquer la plus forte résilience des populations à migration partielle face aux variations environnementales par rapport aux populations strictement résidentes ou migratrices. Toutefois, étant donné les différences de stratégies chez le saumon Atlantique et la truite commune, nos résultats suggèrent que la truite a une meilleure capacité de réponse aux changements environnementaux et un niveau de résilience plus élevé que le saumon Atlantique / This thesis investigates the influence of the tactic diversity on population dynamics in two partially migratory salmonids: Atlantic salmon, Salmo salar and brown trout, Salmo trutta. These two species have high ecological and economic values but the role of migrant and resident individuals on population dynamics and resilience to environmental changes is currently largely unknown. I undertook a multidisciplinary approach combining demographic, genetic, and modeling tools to address these issues in populations from France. I found that tactic determination is partly plastic as juveniles can respond to environmental variations by migrating. In addition, this thesis showed that tactics diversity in partially migratory populations enables a better use of favorable environmental conditions and buffer the effects of unfavorable conditions on their dynamics.These two processes might promote a higher resilience of partially migratory populations to environmental change, including anthropogenic effects, than in solely migratory or resident populations. Nonetheless, given the different strategies in Atlantic salmon and brown trout, my results suggested that brown trout should have better abilities to response to environmental changes and a higher level of resilience than Atlantic salmon.