On the dynamics of a class of multi-group models for vector-borne diseases

The resurgence of vector-borne diseases is an increasing public health concern, and there is a need for a better understanding of their dynamics. For a number of diseases, e.g. dengue and chikungunya, this resurgence occurs mostly in urban environments, which are naturally very heterogeneous, particularly due to population circulation. In this scenario, there is an increasing interest in both multi-patch and multi-group models for such diseases. In this work, we study the dynamics of a vector borne disease within a class of multi-group models that extends the classical Bailey-Dietz model. This class includes many of the proposed models in the literature, and it can accommodate various functional forms of the infection force. For such models, the vector-host/host-vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases. Under the assumption that the contact network is strongly connected, we can define the basic reproductive number $\mathcal{R}_0$ and show that this system has only two equilibria: the so called disease free equilibrium (DFE); and a unique interior equilibrium---usually termed the endemic equilibrium (EE)---that exists if, and only if, $\mathcal{R}_0>1$. We also show that, if $\mathcal{R}_0\leq1$, then the DFE equilibrium is globally asymptotically stable, while when $\mathcal{R}_0>1$, we have that the EE is globally asymptotically stable

Study of Virus Dynamics by Mathematical Models

This thesis studies virus dynamics within host by mathematical models, and topics discussed include viral release strategies, viral spreading mechanism, and interaction of virus with the immune system. Firstly, we propose a delay differential equation model with distributed delay to investigate the evolutionary competition between budding and lytic viral release strategies. We find that when antibody is not established, the dynamics of competition depends on the respective basic reproduction numbers of the two viruses. If the basic reproductive ratio of budding virus is greater than that of lytic virus and one, budding virus can survive. When antibody is established for both strains but the neutralization capacities are the same for both strains, consequence of the competition also depends only on the basic reproduction numbers of the budding and lytic viruses. Using two concrete forms of the viral production functions, we are also able to conclude that budding virus will outcompete if the rates of viral production, death rates of infected cells and neutralizing capacities of the antibodies are the same for budding and lytic viruses. In this case, budding strategy would have evolutionary advantage. However, if the antibody neutralization capacity for the budding virus is larger than that for the lytic virus, lytic virus can outcompete provided that its reproductive ratio is very high. An explicit threshold is derived. Secondly, we consider model containing two modes for viral infection and spread, one is the diffusion-limited free virus transmission and the other is the direct cell-to-cell transfer of viral particles. By incorporating infection age, a rigorous analysis of the model shows that the model demonstrates a global threshold dynamics, fully described by the basic reproduction number, which is identified explicitly. The formula for the basic reproduction number of our model reveals the effects of various model parameters including the transmission rates of the two modes, and the impact of the infection age. We show that basic reproduction number is underestimated in the existing models that only consider the cell-free virus transmission, or the cell-to-cell infection, ignoring the other. Assuming logistic growth for target cells, we find that if the basic reproduction number is greater than one, the infection can persist and Hopf bifurcation can occur from the positive equilibrium within certain parameter ranges. Thirdly, the repulsion effect of superinfecting virion by infected cells is studied by a reaction diffusion equation model for virus infection dynamics. In this model, the diffusion of virus depends not only on its concentration gradient but also on the concentration of infected cells. The basic reproduction number, linear stability of steady states, spreading speed, and existence of traveling wave solutions for the model are discussed. It is shown that viruses spread more rapidly with the repulsion effect of infected cells on superinfecting virions, than with random diffusion only. For our model, the spreading speed of free virus is not consistent with the minimal traveling wave speed. With our general model, numerical computations of the spreading speed shows that the repulsion of superinfecting vision promotes the spread of virus, which confirms, not only qualitatively but also quantitatively, some recent experimental results. Finally, the effect of chemotactic movement of CD8+ cytotoxic T lymphocytes (CTLs) on HIV-1 infection dynamics is studied by a reaction diffusion model with chemotaxis. Choosing a typical chemosensitive function, we find that chemoattractive movement of CTLs due to HIV infection does not change stability of the positive steady state of the model. However, chemorepulsion movement of CTLs destabilizes the positive steady state as the strength of the chemotactic sensitivity increases. In this case, Turing instability occurs, which can be Hopf bifurcation or steady state bifurcation, and spatial heterogeneous patterns may form

Use of climate in a simple entomological framework to improve dynamic simulation and forecast of malaria transmission

Malaria is a serious and life-threatening mosquito-borne disease that every year affects over 200 million individuals and causes 400,00 deaths. An additional 0.5 billion people globally are at risk of malaria infection. The unique role of climate in influencing malaria transmission outcomes across individual communities by acting on multiple dimensions of the malaria vector and parasite ecology has been long recognized. This recognition has led to the development of explicit and implicit climate-driven models of malaria transmission designed to better understand and predict patterns of population vulnerability and uncover potential challenges to malaria control. However, existing implicitly-forced process-based models of malaria have relied on indirectly correlated predictors of malaria transmission, instead of direct relationships among climate, vector entomology and parasite ecology. The lack of biologically-motivated modulation of malaria transmission compromises meaningful interpretation of the ecological role played by climate in malaria transmission. Similarly, the specific influence of climate on vector and parasite dynamics is obscured, limiting the utility of these simple and powerful model forms. This dissertation focuses on elaborating the direct ecological relationships between climate, the malaria vector and parasite to enhance the ecological utility of lower dimensional mathematical models of malaria transmission. In the 2nd chapter of this thesis, a climate-driven entomological modeling framework is developed, consisting of a simple dynamic model that explicitly tracks malaria transmission in human populations and implicitly represents the malaria force of infection through climate-regulation of multiple aspects of the Entomological Inoculation Rate (EIR). The EIR-model construct is found to accurately capture seasonal malaria dynamics under free-simulation, when coupled to local rainfall and temperature climatology across multiple local regions in Rwanda. Furthermore, local rainfall modulation of sub-adult survivorship is found to be a more critical driver of seasonal malaria dynamics than other environmentally-regulated components of EIR. In chapter 3, the model framework is paired with data assimilation methods to dynamically simulate interannual malaria incidence in Rwanda, infer parameters of malaria transmission and validate the malaria model. Results indicate that the implicitly-forced transmission model is able to reproduce interannual and seasonal malaria incidence at regional and local scales. However, accuracy of model description of malaria incidence is more varied at the more resolved local level. Intensified malaria control efforts during the later years of the study are suspected to increase the discrepancy between the vector and parasite dynamics dictated by climate and the observed widespread decline in malaria activity in the region. Nonetheless, the parameters of transmission identified across populations in Rwanda were comparable to existing estimates of malaria, further validating the transmission model and data assimilation approach. For the 4th chapter, a state-of-the-art Bayesian inference forecasting system for the EIR-model framework is developed, as well as a multi-model forecasting system consisting of weighted-average predictions from the dynamic malaria model and historical expectance predictions. Retrospective forecasts of four years of malaria data from 42 regions in Rwanda indicate that the model-inference forecasting system predicts malaria incidence more accurately than historical expectance alone, particularly for predictions with 1-6 weeks lead times. Although slightly less skillful, the multi-model system was found to substantively enhance forecast reliability of the EIR-model system, bolstering the utility of the malaria model as a robust forecaster of malaria in the region. The concluding chapter describes areas for improving the specification of the parsimonious model construct. The need to include malaria control coverage data as exogenous forces of transmission, non-climate drivers and alternate sources of climate exposure that support transmission are highlighted. Future works on forecast calibration needed to improve model performance for real-time prediction are also detailed. In addition, areas for application within information systems for evaluating malaria risk and for advising malaria control efforts, specifically relating to local variability in malaria burden and characterization of entomological drivers of local malaria, are identified and further discussed. The model systems developed in this thesis advance the capabilities of lower dimension dynamic models to connect the ecological drivers of malaria transmission to climate variation. Such process-based formulations could provide better climate-driven descriptions of malaria, while limiting model complexity, without compromising representation of entomological relationships that are potentially valuable for improved understanding and control of malaria transmission

Virus Adaptation at Different Levels: Study on the Evolutionary Effects of Mutations, Host Population Genetic Structure and Environmental Factors in Potyviruses

Tesis por compendio[ES] La evolución experimental nos permite comprobar postulados teóricos y realizar observaciones que ayuden a incrementar nuestro conocimiento sobre la evolución. Este trabajo tiene como objetivo estudiar la evolución de los virus utilizando enfoques experimentales. Los virus muestran una alta capacidad de evolución, lo que los convierte en modelos perfectos para abordar cuestiones evolutivas con bastante rapidez. Los procesos subyacentes a la evolución y adaptación de los patógenos se rigen por muchos factores: desde la naturaleza intrínseca del virus hasta componentes ambientales que afectan al hospedador, al patógeno y la interacción entre ambos. En esta tesis utilizamos un patosistema formado por una planta y un potyvirus (virus de (+)ssRNA) para explorar cómo diferentes factores bióticos y abióticos modulan la evolución del virus. Primero, exploramos los efectos biológicos de las mutaciones en una proteína del potyvirus, la cual es un componente esencial del complejo de replicación viral. Revelamos las limitaciones evolutivas que operan sobre esta proteína, y que son consecuencia de un equilibrio evolutiva entre la acumulación dentro del huésped y la gravedad de los síntomas. En segundo lugar, examinamos los efectos de la estructura genética de la población del huésped sobre la evolución del virus: evolucionamos virus en poblaciones genéticamente homogéneas de plantas con diferentes susceptibilidades a la infección y en una población heterogénea. Con este trabajo ilustramos cómo la diversidad genética de huéspedes en un ecosistema afecta la adaptación del virus, ya que los virus se especializaron más rápidamente en poblaciones homogéneas pero fueron más patógenos en poblaciones heterogéneas. Finalmente, estudiamos el impacto del ambiente sobre la interacción virus-planta. Para esta parte, primero revisamos los posibles efectos beneficiosos de la infección por virus en ciertos entornos hostiles para la planta. Posteriormente estudiamos el efecto de la sequía, una condición ambiental con una incidencia cada vez mayor y que se sabe afecta la fisiología del huésped. Por lo tanto, evolucionamos un virus en huéspedes bajo condiciones de sequía o de riego abundante. Los virus adaptados en condiciones de sequía conferían una mayor tolerancia a la sequía a la planta huésped a través de alteraciones específicas en la expresión génica del huésped y la señalización hormonal. En general, esta tesis contribuye al aumento del conocimiento en biología evolutiva de los virus de ARN de plantas.[CA] L'evolució experimental ens permet comprovar postulats teòrics i realitzar observacions que ajuden a incrementar el nostre coneixement sobre l'evolució. Aquest treball té com a objectiu estudiar l'evolució dels virus utilitzant enfocaments experimentals. Els virus mostren una alta capacitat d'evolució, la qual cosa els converteix en models perfectes per a abordar qüestions evolutives amb bastant rapidesa. Els processos subjacents a l'evolució i adaptació dels patògens es regeixen per molts factors: des de la naturalesa intrínseca del virus fins a components ambientals que afecten l'hoste, al patogen i la interacció entre tots dos. En aquesta tesi utilitzem un patosistema format per una planta i un potyvirus (virus de (+)ssRNA) per a explorar com diferents factors biòtics i abiòtics modulen l'evolució del virus. Primer, explorem els efectes biològics de les mutacions en una proteïna del potyvirus, la qual és un component essencial del complex de replicació viral. Revelem les limitacions evolutives que operen sobre aquesta proteïna, i que són conseqüència d'un equilibri evolutiva entre l'acumulació dins de l'hoste i la gravetat dels símptomes. En segon lloc, examinem els efectes de l'estructura genètica de la població de l'hoste sobre l'evolució del virus: evolucionem virus en poblacions genèticament homogènies de plantes amb diferents susceptibilitats a la infecció i en una població heterogènia. Amb aquest treball il·lustrem com la diversitat genètica d'hostes en un ecosistema afecta l'adaptació del virus, ja que els virus es van especialitzar més ràpidament en poblacions homogènies però van ser més patògens en poblacions heterogènies. Finalment, estudiem l'impacte de l'ambient sobre la interacció virus-planta. Per a aquesta part, primer revisem els possibles efectes beneficiosos de la infecció per virus en uns certs entorns hostils per a la planta. Posteriorment estudiem l'efecte de la sequera, una condició ambiental amb una incidència cada vegada major i que se sap afecta la fisiologia de l'hoste. Per tant, evolucionem un virus en hostes sota condicions de sequera o de reg abundant. Els virus adaptats en condicions de sequera conferien una major tolerància a la sequera a la planta hoste a través d'alteracions específiques en l'expressió gènica de l'hoste i la senyalització hormonal. En general, aquesta tesi contribueix a l'augment del coneixement en biologia evolutiva dels virus d'ARN de plantes.[EN] Experimental evolution allows us to test theoretical postulates and make observations that help increase our knowledge about Evolution. This work aims to use experimental approaches to study the evolution of viruses. Viruses have a high degree of evolvability, which makes them perfect subjects to address evolutionary questions quite rapidly. The underlying processes of pathogen evolution are governed by many factors. These factors can be affecting the virus adaptation at different levels: from the intrinsic virus nature to environmental factors affecting the host, the pathogen and the interaction between both. In this thesis, we used a pathosystem formed by a plant and a potyvirus (+ssRNA virus). Using this pathosystem we have explored how different factors modulate the virus evolution. First, we explored the biological effects of mutations in a potyvirus protein that is an essential component of the virus replication complex. We unveiled the evolutionary constraints on this viral protein, with an evolutionary tradeoff between within-host accumulation and severity of symptoms. Second, we examined the effects of the host population genetic structure on virus evolution: we evolved viruses in homogeneous populations of plants with different viral susceptibilities and in a heterogeneous population. With this work we illustrated how the genetic diversity of hosts in an ecosystem affects virus adaptation, as viruses specialized faster in homogeneous populations but were more pathogenic in heterogeneous ones. Finally, we studied the impact of the environment. For this part we first reviewed the possible beneficial effects of virus infection under certain environments. Afterwards we studied the effect of drought, an environmental condition with a predicted increased incidence and known to affect the host physiology. Therefore, we evolved a virus in host under either well-watered or drought conditions. The viruses adapted under drought conditions conferred an increased drought tolerance to the host plant through specific alterations in host gene expression and hormonal signaling. Overall, this thesis contributed to the increase in knowledge in evolutionary biology of plant RNA viruses.González Miguélez, R. (2021). Virus Adaptation at Different Levels: Study on the Evolutionary Effects of Mutations, Host Population Genetic Structure and Environmental Factors in Potyviruses [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/178154TESISCompendi

Disruption and disease: How does population management affect disease risk in wild bird populations?

Despite the ubiquity of wildlife management, from reintroductions and supplemental feeding to culling and habitat destruction, very little is known of the effects of management practices on species’ social dynamics. Species’ social structure has the potential to affect not only behaviour and evolution but also the transmission of information or disease. Understanding the effects of population management on social behaviour and organisation is a key step in understanding these species’ ecology. This thesis examines the differences between individuals’ roles in the social structure and what this means for the transmission of disease. It demonstrates how similarity in movement behaviour scales with increasing social circles, how seasonality in movement and seasonality in association rates covary as well as detailing post-cull behavioural changes. It finds that there is the potential for certain individuals (most likely non-breeding individuals) to transmit infection far and wide. It reveals the similarities in movement behaviour and body condition that birds share with their pair and social group. It emphasises the importance of autumn and winter movement in the transmission of infectious disease and it follows the short- and long-term changes in social structure and movement behaviour following a cull. Cull survivors were observed to retain a higher proportion of associations with their previous associates and moved less far in the year following the cull than in the year preceding it. This is the first application of social network analysis to quantify social structure before and after culling. The findings suggest that culling an infected population may facilitate rather than constrain the transmission of disease

Statistical physics of vaccination

Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination–one of the most important preventive measures of modern times–is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Pest and Pathogen Control: Strategic, Tactical, and Policy Models

This book describes mathematical models and systems analysis techniques applied to the study of insect pest, plant pathogens, and human diseases. The research programs of over 40 scientists from all over the world are compared and contrasted in detail to provide a state-of-the-art review on how such modeling can increase the effectiveness of more traditional ecological, biological, and chemical control methods. This is the first time such a synthesis has been attempted, and arises in part from a conference hosted by the International Institute for Applied Systems Analysis, Laxenburg, Austria. Papers from this event, plus additional solicited material, have been grouped by Professor Conway into three sections representing strategic, tactical, and policy decision models. An introduction and three linking chapters are provided to place these models in context. Discussing specific case histories in these mathematical terms and the consequent transfer of insights and methods will be of long-term interest to both professional and academic applied entomologists, plant pathologists, medical epidemiologists, applied ecologists, and systems analysts