In an infectious disease with a long infectious period (which can be the entire life for some diseases), the infectivity of individuals may change due to different reasons. For example, infected individuals may receive treatment and their level of infectivity can reduce depending on the efficacy of the treatment. Or, infected individuals may change their behaviour and reduce their activity once the disease is diagnosed, leading to a reduction of their infectivity. Treated individuals may stop getting treatment, and return to the infective class at a rate depending on how long they have been receiving treatment. In this thesis, a compartmental model consisting of three compartments (susceptibles, infectives and treated infectives) is formulated to study the effect of treatment on the transmission dynamics of a disease. Continuous and discrete treatment-age-structured models are derived and the asymptotic behaviour of the system is studied and the basic reproduction number is determined. / October 2016

Despite long-term study, the mechanism explaining the parapatric distribution of two Australian reptile ticks species, Bothriocroton hydrosauri and Amblyomma limbatum, is not understood. This project aimed to use molecular genetic data to investigate aspects of the population biology of these two tick species, such as population structure and dispersal, to gain further insights into the cause and maintenance of this parapatric boundary. I developed and subsequently tested for Mendelian inheritance a suite of B. hydrosauri and A. limbatum species-specific microsatellites markers. Pedigree analysis showed one B. hydrosauri locus and all of the A. limbatum loci to be inherited in a non-Mendelian manner. Thus I could not investigate A. limbatum population structure and focused solely on B. hydrosauri. The first part of this study tested predictions of a model formulated to explain B. hydrosauri transmission dynamics. The “ripple” model, based on detailed ecological and behavioural data on B. hydrosauri and Tiliqua rugosa, B. hydrosauri’s most common host, predicts higher relatedness among larvae than among nymphs or adults on a host, and significant spatial autocorrelation in larvae extending further than for the later life stages. The model also predicts that adult ticks are likely to encounter related partners and that this will generate inbreeding within the population. I tested those predictions using nine microsatellite loci on a sample of 848 ticks (464 larvae, 140 nymphs and 244 adults) collected from 98 T. rugosa hosts at the northern edge of B. hydrosauri’s distribution range. My data did support all of the predictions of the “ripple” model and indicated that the dynamics of transmission among hosts play an important role in parasite population structure. The second part of this project focused on investigating the population genetic structure of B. hydrosauri at the edge of its geographic range and testing the predictions of a population model derived to explain B. hydrosauri’s parapatric boundary with A. limbatum. The “ridge and trough” model suggested the tick population was organised spatially into a series of “ridges” where tick density was high and “troughs” where it was low. Genetically, the expectation was to find clusters of more closely related individuals associated with the ridges. Cluster analysis of microsatellite allele frequencies and analysis of molecular variance of mitochondrial haplotype frequencies revealed the presence of four genetic clusters within a sample of 244 B. hydrosauri adults. As the highly genetically divergent clusters had overlapping distributions, and in some cases were syntopic, the genetic population structure predicted for these ticks by the “ridge and trough” model was not observed. Several explanations were considered for the observed B. hydrosauri genetic population structure, but syntopy of the clusters suggested that assortative mating is the most likely. I speculated that the clusters have formed in allopatry, when the environment was extremely heterogeneous, such that the ticks (and their hosts) were confined to isolated patches of high-quality habitat. Given sufficient time, this could have resulted in reproductive incompatibility between ticks occupying different patches. The population structure I uncovered indicates subsequent secondary recontact of divergent groups. Although my study allowed for a better understanding of B. hydrosauri biology and population structure, the reasons for the parapatric distributions of B. hydrosauri and A. limbatum are still unclear. Further research should focus on investigating the population genetic structure of A. limbatum at the edge of its range, as well as on performing a larger-scale study of B. hydrosauri population genetic structure and a more detailed investigation of the applicability of the “ridge and trough” model to this tick species. Moreover, it will be useful to inspect the population structure of both these species within the centers of their ranges and compare these findings with population structure found at the edge of the range.

Endosymbiosis is a pervasive phenomenon that has been a powerful force in insect evolution. In many well studied insect-bacterial associations, the bacteria can serve as reproductive manipulators, nutritional mutualists or defenders of their hosts. Fungi are also frequently associated with insects, and initial estimates suggest that these fungi are hyperdiverse. Saving a handful of examples, however, the functions of these fungi within insect hosts are largely unknown. This dissertation begins with a review that lays the conceptual groundwork for understanding bacterial and fungal endosymbiosis in insects. I make predictions about why one versus the other microbe might serve the insect, given any unique physiological, ecological or evolutionary conditions. I then aim to derive insights about microbial symbiosis by focusing on a particular system, that of brownbanded cockroaches, Supella longipalpa (Blattaria: Blattellidae) and their specialist wasp parasitoids, Comperia merceti (Hymenoptera: Encyrtidae). Here, I identify the symbiotic community of these two insects by using both culture-dependent and independent methods to characterize the vertically transmitted bacterial and fungal associates. Finally, I show that a heritable fungus in C. merceti, long presumed to be a mutualist, is parasitic under laboratory conditions: infected wasps incur fitness costs for housing the fungal symbiont relative to uninfected wasps. Additionally, although the fungus is not horizontally transmitted sexually, it is readily horizontally transmitted from the offspring of infected females to those of uninfected females that are using the same host.

This thesis is concerned with the structure, analysis and numerical solution of the mathematical models used to estimate the transmission dynamics of the Human Immunodeficiency Virus (HIV)) the causative agent of Acquired Immune Deficiency Syndrome (AIDS). Investigations show that the devised deterministic mathematical models in term of system of first-order non-linear ordinary differential equations (ODEs) follow the stochastic nature of the problem at any time. In this thesis a generic form of the deterministic mathematical models is introduced which mirrors the transmission dynamics of HIV/AIDS in populations with different states of affairs, which leads to the division of large-scale and complex mathematical models. When analysing and;or solving a large-scale system of ODEs numerically, the key element in speeding up the process is selecting the maximum possible time step. This work introduces some new techniques used to estimate the maximum possible time step, avoiding the appearance of chaos and divergence in the solution when they are not features of the system. The solution to these mathematical models are presented graphically and numerically, aiming to identify the effect of the anti-HIV therapies and sex education in controlling the disease. The numerical results presented in this thesis indicate that lowering the average number of sexual partners per year is more effective in controlling the disease than the current anti-HIV treatments. For the purpose of this study the mathematical software 'Mathematica 3.0' was used to solve the system of differential equations, modelling HIV/AIDS propagation. This package also provided the graphical detail incorporated in the thesis.

This thesis is based on the use of mathematical theories, modelling, and simulations to study the transmission dynamics of HIV/AIDS in the presence of PrEP (pre-exposure prophylaxis) in the MSM (men who have sex with men) population in the United States. A new deterministic model for HIV/AIDS that incorporates PrEP is designed and used to assess the population-level impact of the use of PrEP on the transmission dynamics within an MSM population. Conditions for the effective control (or elimination) and persistence of HIV/AIDS in the MSM population are determined by rigorously analyzing this model. Uncertainty and sensitivity analysis is carried out to determine the effect of the uncertainties in the parameter values on the response variable (the associated reproduction number) and to identify the top-five parameters that have the most effect on the disease transmission dynamics. Numerical simulations show that HIV burden decreases with increasing PrEP coverage. / October 2015

The thesis is based on the use of mathematical modeling and analysis to gain insightinto the transmission dynamics of malaria in a community. A new deterministic model for assessing the role of age-structure on the disease dynamics is designed. The model undergoes backward bifurcation, a dynamic phenomenon characterized by the co-existence of a stable disease-free and an endemic equilibrium of the model when the associated reproduction number is less than unity. It is shown that adding age-structure to the basic model for malaria transmission does not alter its essential qualitative dynamics. The study is extended to incorporate the use of anti-malaria drugs. Numerical simulations of the extended model suggest that for the case when treatment does not cause drug resistance (and the reproduction number of each of the two strains exceed unity), the model undergoes competitive exclusion. The impact of various effectiveness levels of the treatment strategy is assessed.

The thesis is based on the use of mathematical modeling and analysis to gain insightinto the transmission dynamics of malaria in a community. A new deterministic model for assessing the role of age-structure on the disease dynamics is designed. The model undergoes backward bifurcation, a dynamic phenomenon characterized by the co-existence of a stable disease-free and an endemic equilibrium of the model when the associated reproduction number is less than unity. It is shown that adding age-structure to the basic model for malaria transmission does not alter its essential qualitative dynamics. The study is extended to incorporate the use of anti-malaria drugs. Numerical simulations of the extended model suggest that for the case when treatment does not cause drug resistance (and the reproduction number of each of the two strains exceed unity), the model undergoes competitive exclusion. The impact of various effectiveness levels of the treatment strategy is assessed.

[ES] Desde tiempos inmemorables en la historia de la humanidad las enfermedades de transmisión sexual (ETSs) han sido una gran amenaza para la salud pública. Las preocupaciones comienzan en la edad moderna con pandemias tales como la sífilis, cuya propagación ocurre en Europa a comienzos del siglo XVI. El virus de papiloma humano (VPH) es la causa directa de más de medio millón de casos nuevos de cáncer de cuello de útero, el segundo más maligno entre mujeres y una de las principales causas de muerte por cáncer en todo el mundo. Además causa verrugas anogenitales y otras enfermedades relacionadas. En este trabajo estudiamos el contagio del VPH en una red de contactos sexuales. Para predecir la evolución de este tipo de enfermedades, necesitamos un modelo fiable de la red social subyacente sobre el que la infección prolifera. Hemos construido una red de parejas sexuales durante toda la vida basada en datos demográficos y encuestas sobre hábitos sexuales. La mayoría de los enfoques para modelizar ETSs por lo general y del VPH en particular, se hacen usando modelos clásicos donde la hipótesis de mezcla homogénea (todo el mundo puede transmitir a todo el mundo) es asumida de manera implícita. Sin embargo, la mezcla homogénea no es una hipótesis razonable y las consecuencias de estas suposiciones se ven de hecho, en que los efectos de los calendarios de vacunación contra el VPH se detectan en Australia mucho antes de lo que los modelos clásicos predijeron. Hay un debate sobre la conveniencia de la vacunación de los niños. Elbasha et al. encontraron evidencias de que la vacunación en niños podría llegar a ser coste-efectiva. En nuestro modelo consideramos poblaciones tanto de hombres que solo tienen relaciones con mujeres y que las tienen entre ellos, permitiéndonos sacar conclusiones al respecto. Con nuestro modelo simulamos y llevamos a cabo campañas de vacunación de modo que podemos sacar conclusiones atendiendo a las mejores estrategias. Estos resultados pueden ayudar a los responsables de Salud Pública a tomar decisiones apropiadas con respecto al VPH. / [CAT] Des de temps inmemorables en la història de la humanitat les malalties de transmissió sexual (MTSs) han sigut una gran amenaça per a la salut pública. Les preocupacions comencen en l'edat moderna amb pandèmies com ara la sífilis, la propagació de la qual ocorre a Europa al començament del segle XVI. El virus de papilloma humà (VPH) és el causant directe de més de mig milió de casos nous de càncer de coll d'úter, el segon mes maligne entre dones i una de les principals causes de mort per càncer en tot el món. A més causa berrugues anogenitales i altres malalties relacionades. En este treball estudiem la dinàmica de transmissió del VPH en una xarxa de contactes sexuals. Per a predir l'evolució d'este tipus de malalties, necessitem un model fiable de la xarxa social subjacent sobre la qual la infecció prolifera. Hem construït un xarxa de parelles sexuals durant tota la vida basada en dades demogràfiques i enquestes sobre hàbits sexuals. La majoria dels enfocaments per a modelizar MTSs generalment i del VPH en particular, es fan usant models clàssics on la hipótesi de mescla homogènia (tot el món pot transmetre a tot el món) és assumida de manera implícita. No obstant això la mescla homogènia no és una hipòtesi raonable i les conseqüències d'estes suposicions es veuen de fet, en que els efectes dels calendaris de vacunació contra el VPH es detecten a Austràlia molt abans del que els models clàssics van predir. / [EN] Sexually transmitted diseases (STDs) have been a major public health threat for a long time in human history. Modern concerns about STD began with the pandemic of syphilis which spread over Europe in the early sixteenth century. The human papillomavirus (HPV) is the direct cause of more than half million new cases of cervical cancer, the second most common malignancy among women and a leading cause of cancer death worldwide. It also causes anogenital warts and other related diseases. In this work we have studied the transmission dynamics of HPV over a sexual contacts network. In order to predict the evolution of these kind of diseases, we need a reliable model of the underlying social network in which the infection spreads. We have built a lifetime sexual partners (LSP) network based on demographic data and surveys about sexual habits. Most of the modeling approaches to STD in general and HPV in particular, are done using classical models where the hypothesis of homogeneous mixing (everybody can transmit a disease to everybody) is assumed. However, homogeneous mixing is not a reasonable hypothesis and consequences of this assumption can be seen, for instance, in that the effects of vaccination schedules against HPV have been detected in Australia much sooner than what the classical models predicted. There is a debate concerning the vaccination of young men. Elbasha et al. found some evidences that the vaccination of boys could also be cost-effective. In our model we consider both heterosexual men, and men who have sex with men (MSM) populations and the connections among them letting us to study this matter. With our model simulate and carry out vaccination campaigns in order to figure out the best strategies. All these results can be useful for policy makers in Public Health to make appropriate decisions respect to HPV. / Sánchez Alonso, V. (2019). Building networks of sexual partners. Application for the study of the transmission dynamics of Human Papillomavirus (HPV) [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/124344 / TESIS

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Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world's human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood, although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. The analyses based on the deterministic model are verified by stochastic simulation near the thresholds of the parameters. / Master of Science