Variabilités des descripteurs physiques, chimiques et biologiques d'un réservoir de stokage (lagunage mixte, en Slimane - Maroc)

L'étude des variations des descripteurs physiques, chimiques et biologiques des eaux d'un réservoir de maturation du lagunage mixte (Ben Slimane, Maroc), a montré une augmentation des valeurs de certaines variables (oxygène dissous, transparence) après le 36ème jour de rétention en raison d'une remise en solution.A 36 jours de rétention, la chute des teneurs de la DBO5, de la DCO, des composés azotés (NH4+, NO3-, NTK) et phosphorés (PO43-, PT), et l'augmentation du pH, de l'oxygène dissous et de la transparence laissent présager une maturation à cette date de mesure. Les densités planctoniques enregistrées à ce niveau sont les plus basses.Au-delà de ce stade de maturation, le phytoplancton prolifère avec dominance d'Euglena viridis qui montre un pic de densité (4,1.106 Individus/m3) le 81ème jour. Le début de sa phase exponentielle de croissance est observé à partir du 18ème jour de maturation. La densité cellulaire est ensuite atténuée vraisemblablement en raison de la diminution de la charge organique (DBO5 et DCO) après le 81ème jour et de l'intensité de broutage par le zooplancton herbivore surtout Acanthocyclops robustus qui montre son maximum de croissance le 138ème jour.Après le 81ème jour de maturation, Euglena viridis est remplacée par deux espèces de Chlorophycées (Pediastrum boryanum et Ankyra judai) dont le maximum de densité (91% de la densité algale totale) est atteint le 138ème jour. La prolifération de ces espèces coïncide avec des valeurs en nitrates dépassant 10,6 mg N/L.A la fin de cette période d'étude (le 138ème jour), le zooplancton est à sa prolifération maximale (106 individus/m3). Il est dominé par Acanthocyclops robustus avec présence de Nauplii et de Daphnia magna. Les Rotifères présents depuis le début de la maturation disparaissent à 138 jours de rétention. L'étude bactériologique a révélé un rendement épuratoire remarquable atteignant 100% pour les coliformes fécaux et les streptocoques fécaux.A study of physical, chemical and biological descriptors of the water in the storage reservoir of a combined stabilization pond (Ben Slimane, Morocco), during maturation, showed an improvement of the purification output for some variables after 36 days of retention. Such an environment, rich with a range of different nutrients, allowed an optimal development of plankton characterized by a high species diversity that decreased with time. Zooplankton development seemed to be limited by poor phytoplankton biomass. However, trophic factors such as nutrients and temperature affected the evolution of planktonic species.After 36 days of retention, the decrease in BOD5, COD, NH4+, NO3-, total Kjeldahl nitrogen (TNK), PO43-, total phosphorus (TP), and the increase in pH, dissolved oxygen and transparency, suggested that maturation had been reached at this level. Simultaneously, phyto- and zooplankton were present in low densities. Nevertheless, beyond this stage of maturation, phytoplankton proliferation occurred, dominated by Euglena viridis whose exponential phase of growth began at the 18th day of maturation and reached a maximum density after 81 days (4.1x106 individus/m3). A low proportion of Chlorophyte species was observed, represented by Pediastrum boryanum and Ankyra judai. The zooplankton community was dominated by two species of Cladocera (Daphnia magna and Diaphanosoma sp).The increase in Euglena viridis density up to 81 days coincided with zooplanktonic proliferation constituted exclusively by Rotifers (Brachionus calyciflorus and Polyarthra remata). At 111 days of retention, the zooplankton community consisted of Copepods (Acanthocyclops robustus), which reappeared at this stage, as well as Nauplii Cladocera (Daphnia magna) and residual Rotifers (Brachionus calyciflorus and Polyarthra remata). The remarkable decrease in Euglena density on day 111 and their complete disappearance on day 138 was probably linked to grazing by herbivorous zooplankton and to low organic matter concentrations. Euglena viridis was replaced by two Chlorophytes (Pediastrum boryanum and Ankyra judai) reaching their maximum density (91% of total algal density) on day 138. The proliferation of these species coincided with values exceeding 10.6 mg N/L. Zooplankton were dominated by Acanthocyclops robustus with the presence of Nauplii and Daphnia magna (106individuals/m3). Rotifers were present since the beginning of the maturation, but were absent by 138 days of retention.The qualitative and quantitative changes in phyto- and zooplankton result from factors that control the growth and the loss of these populations. A low growth rate can lead to biomass accumulation if the growth exceeds loss. On the other hand, a low and stable biomass can result from a high growth rate that is compensated by important losses. Zooplankton grazing and algal sedimentation, which are the two main mechanisms related to phytoplankton decline, are two selective processes (POURRIOT et al., 1982). In stabilization ponds, food chains are established that allow water clarity and minimize algal proliferation. The bacteriological study showed a remarkable purification, with reductions reaching 100% for faecal coliforms and faecal Streptococcus

Final Outcome of an Epidemic in Two Interacting Populations

we consider a stochastic model for the spread of an epidemic in a closed population consisting of two groups, in which infectives cannot change their group, but are able to infect outside it. Using the matrix-geometric method we obtain a recursive relationship for the Laplace transform of the joint distribution of the number of susceptibles and infectives in the two groups. We also derive the distribution of the total observed size of the epidemic as well as its duration in the case of a general infection mechanism

On the Qualitative Behaviour of SIR Epidemics with Generalized Infection Rate Functions

We consider an SIR stochastic epidemic model in which new infection occurs at rate f(n)(x,y), where x and y are respectively the number of susceptibles and infectives at time of infection and f(n) is a positive sequence of real functions. Threshold theorems analogous to those of Whittle and Williams are fairly proved for this model. Also we examine the shape of the total size distribution for various values of removal rate and suitable values of other important parameters

Final Outcome of an Epidemic in Two Interacting Populations

we consider a stochastic model for the spread of an epidemic in a closed population consisting of two groups, in which infectives cannot change their group, but are able to infect outside it. Using the matrix-geometric method we obtain a recursive relationship for the Laplace transform of the joint distribution of the number of susceptibles and infectives in the two groups. We also derive the distribution of the total observed size of the epidemic as well as its duration in the case of a general infection mechanism

TRANSITION PROBABILITIES FOR GENERALIZED SIR EPIDEMIC MODEL

Gani and Purdue outlined a matrix-geometric method for determining the total size distribution of an epidemic in a recursive manner. In this article, we explore how this method can be used to study an SIR epidemic model with a generalized mechanism of infection. We are able to obtain an explicit formula for the Laplace transform of the transition probabilities. Using this we derive various other quantities explicitly. Examples of such quantities are the transition probabilities and the expectation of the duration of the epidemic

Final outcome probabilities for SIR epidemic model

We consider an SIR stochastic epidemic model in which new infections occur at rate f(x, y), where x and y are, respectively, the number of susceptibles and infectives at the time of infection and f is a positive sequence of real functions. A simple explicit formula for the final size distribution is obtained. Some efficient recursive methods are proved for the exact calculation of this distribution. In addition, we give a Gaussian approximation for the final distribution using a diffusion process approximation

A Branching Process Approximation of the Final Size of a Multitype Collective Reed-Frost Model

We consider the asymptotic behavior of the final size of a multitype collective Reed-Frost process. This type of models was introduced by [9] and include most known epidemic models of the type SIR (Susceptible, Infected, Removed) as special cases. Under certain conditions, we show that, when the initial number of susceptible is very large and the initial number of infected individuals is finite, the infection process behaves as a multitype Galton-Watson process. This fact is proved using a simple argument based on Bernstein polynomials. We use this result to study the final size of the epidemic