Equilibrium analysis of a yellow Fever dynamical model with vaccination.

We propose an equilibrium analysis of a dynamical model of yellow fever transmission in the presence of a vaccine. The model considers both human and vector populations. We found thresholds parameters that affect the development of the disease and the infectious status of the human population in the presence of a vaccine whose protection may wane over time. In particular, we derived a threshold vaccination rate, above which the disease would be eradicated from the human population. We show that if the mortality rate of the mosquitoes is greater than a given threshold, then the disease is naturally (without intervention) eradicated from the population. In contrast, if the mortality rate of the mosquitoes is less than that threshold, then the disease is eradicated from the populations only when the growing rate of humans is less than another threshold; otherwise, the disease is eradicated only if the reproduction number of the infection after vaccination is less than 1. When this reproduction number is greater than 1, the disease will be eradicated from the human population if the vaccination rate is greater than a given threshold; otherwise, the disease will establish itself among humans, reaching a stable endemic equilibrium. The analysis presented in this paper can be useful, both to the better understanding of the disease dynamics and also for the planning of vaccination strategies

Mathematics of Viral Infections: A Review of Modeling Approaches and A Case-Study for Dengue Dynamics

In this thesis we use mathematical models to study the mechanisms by which diseases spread. Transmission dynamics is modelled by the class of SIR models, where the abbreviation stands for susceptible (S), infected (I) and recovered (R). These models are also called compartmental models, and they serve as the basic mathematical framework for understanding the complex dynamics of infectious diseases. Theory developed for the SIR framework can be applied the real-world dynamics, for instance to the spread of the dengue virus. We look at how parameters such as the as basic reproduction number, R0, drive epidemics by allowing transitions from a disease-free equilibrium (DFE) when R0 1. A case study was carried out to investigate dengue transmission dynamics in a single serotype model by using a vector-to-human compartmental model. Here the approach is to explore the underlying dynamical structures, as well as looking at the projected impact of possible interventions such as vaccines and vector-control measures

Insecticide resistance monitoring : a review of current methology

Introduction: Insecticide resistance continues to pose a serious threat to the control of vector-borne diseases. In the last decades, it has spread across Africa and many countries with high transmission of mosquito-borne diseases. A major handicap in the efforts to control resistance is the limited availability of routine and reliable data, a situation which arises from the fact that many countries with ongoing transmission of vector-borne diseases do not perform routine data collection, or in areas where data are available, there are high levels of inconsistencies in the reported data. Although WHO has put in place guidelines to be followed in performing bioassays to detect resistance, the guidelines are not standard operating procedure and leave room for discretion. Taking into account the importance of effective vector control and the limitation on the number of insecticide classes available, preserving the susceptibility of malaria vectors to the present classes of insecticides is essential in maintaining effective malaria control. The evolution of resistance to insecticides could endanger current and future achievements in controlling malaria. Therefore, the need for proper monitoring interventions equipped with well laid out guidelines cannot be overlooked. Aims and objectives: The main aim was to review existing methodologies employed in insecticide resistance monitoring and identify factors that lead to inconsistencies in data generated in vector control strategies. This overarching aim is divided under three main objectives: i. to assess the effect of bioassays on the test outcome; ii. to assess the influence of the rearing conditions of mosquitoes on bioassay outcomes; and iii. to assess the effect of inter laboratory variability on the outcome of the test. Methods: Using laboratory-bred mosquito colonies, we performed susceptibility experiments with the principal diagnostic bioassays against insecticides mostly used in public health for the control of the major vectors involved in disease transmission to assess the robustness of the bioassays. We also bred mosquito larvae under different conditions to evaluate the effect of changes in environmental factors on the susceptibility of the adults to insecticides. The data generated was extended to a mathematical model to estimate the effects of larval population density on adult survival. The major sources of inter-laboratory differences in data generated in insecticide resistance monitoring activities were also tested by performing the WHO susceptibility assay at multiple centres. Results: The results indicate that the WHO susceptibility and CDC bottle bioassays which are generally used interchangeably for both field and laboratory evaluations of insecticide resistance are highly inconsistent in generating the same results on the same mosquito population. The WHO cone assay also produces different results when the assay is performed at different angles. We also found the breeding conditions during the larval stage significantly affect the susceptibility status of the adult mosquito to insecticides. The mathematical models also showed that larval density significantly affects adult survival. Conclusion: Results from this thesis reinforces the call for proper insecticide resistance monitoring tools and practices. While the problem of insecticide resistance is on the rise, the lack of effective and reliable methods to detect and monitor resistance remains a major concern