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.

A nested model with boosting and waning of immunity from Tilapia Lake Virus infection with distributed resistance to pathogens carrier-state.

This paper proposes and analyzes an immune-structured population model of tilapia subject to Tilapia Lake Virus (TiLV) disease. The model incorporates within-host dynamics, used to describe the interaction between the pathogen, the immune system and the waning of immunity. Individuals infected with a low dose acquire a low immunity level and those infected with a high dose acquire a high level of immunity. Since individuals' immune status plays an important role in the spread of infectious diseases at the population level, the within-host dynamics are connected to the between-host dynamics in the population. We define an explicit formula for the reproductive number [Formula: see text] and show that the disease-free equilibrium is locally asymptotically stable when [Formula: see text], while it is unstable when [Formula: see text]. Furthermore, we prove that an endemic equilibrium exists. We also study the influence of the initial distribution of host resistance on the spread of the disease, and find that hosts' initial resistance plays a crucial role in the disease dynamics. This suggests that the genetic selection aiming to improve hosts' initial resistance to TiLV could help fight the disease. The results also point out the crucial role played by the inoculum size. We find that the higher the initial inoculum size, the faster the dynamics of infection. Moreover, if the initial inoculum size is below a certain threshold, it may not result in an outbreak at the between-host level. Finally, the model shows that there is a strong negative correlation between heterogeneity and the probability of pathogen invasion.

An Age-Structured Model for Tilapia Lake Virus Transmission in Freshwater with Vertical and Horizontal Transmission.

This paper proposes a mathematical model for tilapia lake virus (TiLV) transmission in wild and farmed tilapias within freshwater. This model takes into account two routes of transmission: vertical and horizontal. This latter route integrates both the direct and indirect transmission. We define an explicit formula for the reproductive number [Formula: see text] and show by means of the Fatou's lemma that the disease-free equilibrium is globally asymptotically stable when [Formula: see text]. Furthermore, we find an explicit formula of the endemic equilibria and study its local stability as well as the uniform persistence of the disease when [Formula: see text]. Finally, a numerical scheme to solve the model is developed and some parameters of the model are estimated based on biological data. The numerical results illustrate the role of routes of transmission on the epidemic evolution.