Theoretical Assessment of the Impact of Water Stress on Plants Production: Case of Banana-Plantain.

The aim of this paper is to investigate the role of water stress on plants production. We propose a mathematical model for the dynamics growth of plants that takes into account the concentration of available water in the soil, water stress, plant production and plants compensation. Sensitivity analysis of the model has been performed in order to determine the impact of related parameters on the dynamics growth of plants. We present the theoretical analysis of the model with and without water stress. More precisely, we show that the full model is well-posedness. For each model, we compute the trivial equilibria and derive two thresholds parameters that determine the outcome of water stress within a plantation. Further, we perform numerical simulation on the case of banana-plantain simulations to support the theory. We found that the Hopf bifurcation occurs for a specific value of the water absorption rate of unstressed plants. The impact of the water stress on the banana-plantain production is also numerically investigated. After, the role of the water stress on the plant production is numerically investigated. We found that the water stress can cause about 68.16% of loss of banana-plantain production within a plantation with 1600 rejets initially planted. This suggests that climate change plays a detrimental role on banana-plantains production.

Prediction of pulmonary tuberculosis treatment outcome in a sub-Saharan African context.

Failure to treat many pathogens is a concern. Identifying a priori, patients with potential failure treatment outcome of a disease could allow measures to reduce the failure rate. The objectives of this study were to use the Scoring method to identify factors associated with the tuberculosis unsuccessful treatment outcome and to predict the treatment outcome. A total of 1,529 patients with pulmonary tuberculosis were randomly selected in the city of Douala, Cameroon, this sample was randomly split into two parts: one subsample of 1,200 patients (78%) used as the Development sample, and the remaining of 329 patients (22%) used as the Validation sample. Baseline characteristics associated with unsuccessful treatment outcomes were investigated using logistic regression. The optimal score was based on the Youden's index. HIV positive status, active smoker and non-belief in healing were the factors significantly associated with unsuccessful treatment outcomes (P#x003C;0.05). A model used to estimate the risk of unsuccessful treatment outcome was derived. The threshold probability which maximize the area under the ROC curve was 18%. Patients for whom the risk was greater than this threshold were classified as unsuccessful treatment outcome and the others as successful. HIV positive and active smoking status were associated with death; the non-belief in healing, youth and male gender associated with lost-to-follow-up, TB antecedent and not having TB contact associated with therapeutic treatment failure. To increase the tuberculosis treatment success rate, targeted follow-up could be taken during the treatment for TB patients with previous characteristics.

Coupling the modeling of phage-bacteria interaction and cholera epidemiological model with and without optimal control.

In this work, we assess the impact of the phage-bacteria infection and optimal control on the indirectly transmitted cholera disease. The phage-bacteria interactions are described by predator-prey system using the Smith functional response, which takes into account the number of bacteria binding sites. The study is done in two steps, namely the model without control and the model with control. For the first scenario, we explicitly compute the basic reproduction number R0 which serves as stability threshold and bifurcation parameter. The proposed model exhibits a bi-stability phenomenon via the existence of backward bifurcation, which implies that the classical requirement of bringing the reproduction number under unity, while necessary, is no longer sufficient for cholera elimination from the population. We intuitively introduce a new threshold number N0 needed for the global stability of the disease free equilibrium point which is achieved when R0⩽1 and N0⩽1. It is further shown that the phage absorption is a possible cause of bi-stability, since in its absence, the condition R0⩽1 is sufficient for cholera to die out. The existence of endemic equilibrium points depends on the range of both R0 and N0. Regarding the model extended to an optimal control problem, which involves the use of virulent vibriophages to reduce or eliminate the bacteria population, we use optimal control theory techniques. We establish the conditions under which the spread of cholera can be stopped, and examine the impact of control measures on the transmission dynamic of cholera. The Pontryagin's maximum principle is used to characterize the optimal control. Numerical simulations suggest that, the release of lytic vibriophages can significantly reduce the spread of the disease. We discuss opportunities for phage therapy as treatment of some bacterial-borne diseases without side effects.

Study of the Population Dynamics of Busseola fusca, Maize Pest.

Busseola fusca is a maize and sorghum pest that can cause significant damage to both crops. Given that maize is one of the main cereals grown in the worldwide, this pest is a major challenge for maize production and therefore for the economies of several countries . In this paper , based on the life cycle of B. fusca, we propose a mathematical model to study the population dynamics of this insect pest . A sensitivity analysis using the eFast method was performed to show the most important parameters of the model. We present the theoretical analysis of the model. More precisely, we derive a threshold parameter [Formula: see text], called basic offspring number and show that the trivial equilibrium is globally asymptotically stable whenever [Formula: see text], while if [Formula: see text], the non trivial equilibrium is globally asymptotically stable. The theoretical results are supported by numerical simulations.

Modeling ebola virus disease transmissions with reservoir in a complex virus life ecology.

We propose a new deterministic mathematical model for the transmission dynamics of Ebola Virus Disease (EVD) in a complex Ebola virus life ecology. Our model captures as much as possible the features and patterns of the disease evolution as a three cycle transmission process in the two ways below. Firstly it involves the synergy between the epizootic phase (during which the disease circulates periodically amongst non-human primates populations and decimates them), the enzootic phase (during which the disease always remains in fruit bats population) and the epidemic phase (during which the EVD threatens and decimates human populations). Secondly it takes into account the well-known, the probable/suspected and the hypothetical transmission mechanisms (including direct and indirect routes of contamination) between and within the three different types of populations consisting of humans, animals and fruit bats. The reproduction number R0 for the full model with the environmental contamination is derived and the global asymptotic stability of the disease free equilibrium is established when R0andlt;1. It is conjectured that there exists a unique globally asymptotically stable endemic equilibrium for the full model when R0andgt;1. The role of a contaminated environment is assessed by comparing the human infected component for the sub-model without the environment with that of the full model. Similarly, the sub-model without animals on the one hand and the sub-model without bats on the other hand are studied. It is shown that bats influence more the dynamics of EVD than the animals. Global sensitivity analysis shows that the effective contact rate between humans and fruit bats and the mortality rate for bats are the most influential parameters on the latent and infected human individuals. Numerical simulations, apart from supporting the theoretical results and the existence of a unique globally asymptotically stable endemic equilibrium for the full model, suggest further that: (1) fruit bats are more important in the transmission processes and the endemicity level of EVD than animals. This is in line with biological findings which identified bats as reservoir of Ebola viruses; (2) the indirect environmental contamination is detrimental to human beings, while it is almost insignificant for the transmission in bats.

Optimal control for an age-structured model for the transmission of hepatitis B.

One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention.

Finite-time synchronization of tunnel-diode-based chaotic oscillators.

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel-diode-based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulations followed by pspice experiment are presented to show the feasibility of the proposed method.

[Management of tuberculosis patients in the urban setting: health service delivery and health care-seeking behavior]. / Prise en charge des patients souffrant de la tuberculose en milieu urbain: offre de soins et parcours thérapeutique.

OBJECTIVES: This descriptive and prospective study was designed to determine the incidence of smear-positive pulmonary tuberculosis (PTB+) by health area (HA) in Douala, use of Diagnosis and Treatment Centres (DTCs) and the factors influencing the choice of DTC. METHODS: Over a one-year period, the residence of all PTB+ patients and the DTC at which they were treated were located by means of a GPS system and represented on a geo-referenced health map. Incidence of PTB+ per HA was calculated. Focus group discussions with TB patients were then held in seven of the nineteen DTCs chosen by convenience. RESULTS: The incidence of PTB+ is not randomly distributed between HAs, as the incidence is fivefold higher than the mean in some HAs. More than one half of patients (65%) were not treated in the DTC to which they were designated by the health system. Attendance in a DTC mostly depends on chance decisions based on previous experiences with a health care unit, recommendations from family members, friends or strangers, or the (sometimes erroneous) reference by health care personnel. References rarely follow the logic of the system. CONCLUSION: The provision of health care for TB in the city of Douala and health care-seeking behaviour of patients frequently do not correspond. Information and communication on TB care delivery could make the management of tuberculosis more efficient and more effective.

Global stability analysis for SEIS models with n latent classes.

We compute the basic reproduction ratio of a SEIS model with n classes of latent individuals and bilinear incidence. The system exhibits the traditional behaviour. We prove that if R(0) < or = 1, then the disease-free equilibrium is globally asymptotically stable on the nonnegative orthant and if R (0) > 1, an endemic equilibrium exists and is globally asymptotically stable on the positive orthant.

Controlled synchronization of chaotic systems with uncertainties via a sliding mode control design.

This paper addresses the problem of robust adaptive control for synchronization of continuous-time coupled chaotic systems with uncertainties. A general model is studied using measured output state feedback control. An adaptive controller is designed based on a sliding mode control design. When only the output variable is measurable for synchronization, the adaptive controller is designed by incorporating with an observer. Two numerical examples are presented to show the effectiveness of the proposed chaos synchronization method.