Modelling vector-borne diseases: epidemic and inter-epidemic activities with application to Rift Valley fever

Abstract

In this thesis in order to study the complex dynamics of Rift Valley fever (RVF) we combine two modelling approaches: equation-based and simulation-based modelling. In the first approach we first formulate a deterministic model that includes two vector populations, Aedes and Culex mosquitoes with one host population (livestock), while considering both horizontal and vertical transmissions. An easy applicable expression of the basic reproduction number, R0 is derived for both periodic and non-periodic environment. Both time invariant and time varying uncertainty and sensitivity analysis of the model is carried out for quantifying the attribution of model output variations to input parameters over time and novel relationships between R0 and vertical transmission are determined providing important information useful for improving disease management. Then, we analytically derive conditions for stability of both disease-free and endemic equilibria. Using techniques of numerical simulations we perform bifurcation and chaos analysis of the model under periodic environment for evaluating the effects of climatic conditions on the characteristic pattern of disease outbreaks. Moreover, extending this model including vectors other than mosquitoes (such as ticks) we evaluate the possible role of ticks in the spread and persistence of the disease pointing out relevant model parameters that require further attention from experimental ecologists to further determine the actual role of ticks and other biting insects on the dynamics of RVF. Additionally, a novel host-vector stochastic model with vertical transmission is used to analytically determine the dominant period of disease outbreaks with respect to vertical transmission efficiency. Then, novel relationships among vertical transmission, invasion and extinction probabilities and R0 are determined. In the second approach a novel individual-based model (IBM) of complete mosquito life cycle built under daily temperature and rainfall data sets is designed and simulated. The model is applied for determining correlation between abundance of mosquito populations and rainfall regimes and is then used for studying disease inter-epidemic activities. We find that indeed rainfall is responsible for creating intra- and inter-annual variations observed in the abundance of adult mosquitoes and the length of gonotrophic cycle, number of eggs laid per blood meal, adults age-dependent survival and fight behaviour are among the most important features of the mosquito life cycle with great epidemiological impacts in the dynamics of RVF transmission. These indicators could be of great epidemiological significance by allowing disease control program managers to focus their e orts on specific features of vector life cycle including vertical transmission ability and diapause. We argue that our IBM model is an ideal extendible framework useful for further investigations of other relevant host-vector ecological and epidemiological questions for providing additional knowledge important for improving the length and quality of life of humans and domestic animals.