Modelling Foot and Mouth Disease in the Context of Active Immigrants

This study employs mathematical modeling to analyze the impact of active immigrants on Foot and Mouth Disease (FMD) transmission dynamics. We calculate the reproduction number (R0) using the next-generation matrix approach. Applying the Routh-Hurwitz Criterion, we establish that the Disease-Free Equilibrium (DFE) point achieves local asymptotic stability when R0 α1 and α2) are closely associated with reduced susceptibility in animal populations, underscoring the link between immigrants and susceptibility. Furthermore, our findings emphasize the interplay of disease introduction with population response and adaptation, particularly involving incoming infectious immigrants. Swift interventions are vital due to the limited potential for disease establishment and rapid susceptibility decline. This study offers crucial insights into the complexities of FMD transmission with active immigrants, informing effective disease management strategies.

Assessing Weather Research and Forecasting (WRF) Model Parameterization Schemes Skill to Simulate Extreme Rainfall Events over Dar es Salaam on 21 December 2011

This paper evaluates the skills of physical Parameterization schemes in simulating extreme rainfall events over Dar es Salaam Region, Tanzania using the Weather Research and Forecasting (WRF) model. The model skill is determined during the 21 December 2011 flooding event. Ten sensitivity experiments have been conducted using Cumulus, Convective and Planetary boundary layer schemes to find the best combination and optimize the WRF model for the study area for heavy rainfall events. Model simulation results were verified against observed data using standard statistical tests. The model simulations show encouraging and better statistical results with the combination of Kain-Fritsch cumulus parameterization scheme, Lin microphysics scheme and Asymmetric Convection Model 2 (ACM2) planetary boundary scheme than any other combinations of physical parameterization schemes over Dar es Salaam region.

Formulation of Mathematical Model for TB Transmission in Zoonotic Areas with Existence of Endemic Equilibrium

A mathematical model incorporating animal TB and Human TB transmission is formulated and analysed in order to determine the role of animal TB and human TB in the overall TB transmission and also, to determine the parameters which govern the transmission of the TB disease. The model has five classes namely susceptible, exposed animal TB, and exposed human TB, infectious and recovery. The model assumed that there are two classes for infected individuals, those who acquired TB through animal and those who acquire TB from human. Qualitative results show that the model has the disease-free equilibrium and at least one endemic equilibrium that is locally asymptotically stable. The study includes numerical simulations as a way of supporting the analytical results. Graphical results indicate that animal TB has major contribution on overall TB transmission and the TB transmission can be reduced by ensuring intervention to both Animal TB and Human TB. Furthermore the equations indicate that there is at least one endemic equilibrium which translates that t animal and human have the contribution on TB transmission. This shows that both animals and humans together with fast progressors have contribution on TB transmissions.

Effects of Over-Harvesting and Drought on a Predator-Prey System with Optimal Control

In this paper, a two species predator-prey model is developed where prey is affected by over-harvesting and drought and predator is affected by drought. The intention is to investigate the impact of over-harvesting and drought on predator-prey system, and suggest control strategies to alleviate the problem of loss of prey and predator species due to over-harvesting and drought. The control strategies suggested are creation of reserve areas with restriction of harvesting for controlling over-harvesting and construction of dams for mitigating drought effects. The results obtained from theoretical and numerical simulation of the predator-prey model with harvesting and drought without control strategies showed that, both harvesting and drought affect the predator-prey population negatively. However, the results obtained from numerical simulations of the model with control measures showed that, the use of control strategies one at a time encourages the increase of the prey and predator species to the optimal population size. Furthermore, the best result is obtained when control strategies, creation of reserve areas with restriction of harvesting and construction of dams are applied simultaneously.