On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease

This paper studies the nonnegativity and local and global stability properties of the solutions of a newly proposed SEIADR model which incorporates asymptomatic and dead-infective subpopulations into the standard SEIR model and, in parallel, it incorporates feedback vaccination plus a constant term on the susceptible and feedback antiviral treatment controls on the symptomatic infectious subpopulation. A third control action of impulsive type (or “culling”) consists of the periodic retirement of all or a fraction of the lying corpses which can become infective in certain diseases, for instance, the Ebola infection. The three controls are allowed to be eventually time varying and contain a total of four design control gains. The local stability analysis around both the disease-free and endemic equilibrium points is performed by the investigation of the eigenvalues of the corresponding Jacobian matrices. The global stability is formally discussed by using tools of qualitative theory of differential equations by using Gauss-Stokes and Bendixson theorems so that neither Lyapunov equation candidates nor the explicit solutions are used. It is proved that stability holds as a parallel property to positivity and that disease-free and the endemic equilibrium states cannot be simultaneously either stable or unstable. The periodic limit solution trajectories and equilibrium points are analyzed in a combined fashion in the sense that the endemic periodic solutions become, in particular, equilibrium points if the control gains converge to constant values and the control gain for culling the infective corpses is asymptotically zeroed.This research is supported by the Spanish Government and the European Fund of Regional Development FEDER through Grant DPI2015-64766-R

Dynamics of an SIR Model with Nonlinear Incidence and Treatment Rate

In this paper, global dynamics of an SIR model are investigated in which the incidence rate is being considered as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated). Analytical study of the model shows that the model has two equilibrium points (diseasefree equilibrium (DFE) and endemic equilibrium (EE)). The disease-free equilibrium (DFE) is locally asymptotically stable when reproduction number is less than one. Some conditions on the model parameters are obtained to show the existence as well as nonexistence of limit cycle. Some sufficient conditions for global stability of the endemic equilibrium using Lyapunov function are obtained. The existence of Hopf bifurcation of model is investigated by using Andronov-Hopf bifurcation theorem. Further, numerical simulations are done to exemplify the analytical studies

Estudio del efecto de la vacunación en modelos de epidemias con transmisión estocástica

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Estudios Estadísticos, leída el 15-12-2022Mathematical epidemic models are frequently used in biology for analyzing transmission dynamics of infectious diseases and assessing control measures to interrupt their expansion. In order to select and develop properly the above mathematical models, it is necessary to take into account the particularities of an epidemic process as type of disease, mode of transmission and population characteristics. In this thesis we focus on infectious diseases with stochastic transmission including vaccination as a control measure to stop the spread of the pathogen. To that end, we consider constant and moderate size populations where individuals are homogeneously mixed. We assume that characteristics related to the transmission/recovery of the infectious disease present a common probabilistic behavior for individuals in the population. To assure herd immunity protection, we consider that a percentage of the population is protected against the disease by a vaccine, prior to the start of the outbreak.The administered vaccine is imperfect in the sense that some individuals, who have been previously vaccinated, failed to increase antibody levels and, in consequence, they could be infected. Pathogenic transmission occurs by direct contact with infected individuals. As population is not isolated, disease spreads from direct contacts with infected individuals inside or outside the population...Los modelos matemáticos epidemiológicos se usan frecuentemente en biología para analizar las dinámicas de transmisión de enfermedades infecciosas y para evaluar medidas de control con el objetivo de frenar su expansión. Para poder seleccionar y desarrollar adecuadamente estos modelos es necesario tener en cuenta las particularidades propias del proceso epidémico tales como el tipo de enfermedad, modo de transmisión y características de la población. En esta tesis nos centramos en el estudio de enfermedades de tipo infeccioso con transmisión por contacto directo, que disponen de una vacuna como medida de contención en la propagación del patógeno. Para ello, consideramos poblaciones de tamaño moderado, que permanece constante a lo largo de un brote y asumiremos que los individuos no tienen preferencia a la hora de relacionarse y que las características referentes a la transmisión de la enfermedad se representan en términos de variables aleatorias, comunes para todos los individuos. La población no está aislada y la transmisión del patógeno se produce mediante contacto directo con cualquier persona infectada, tanto de dentro de la población como fuera de ella. Asumimos que, antes del inicio del brote epidémico, se ha administrado la vacuna a un porcentaje suficiente de individuos de la población, de forma que se asegure la inmunidad de rebaño. Consideramos que la vacuna administrada es imperfecta en el sentido que algunos individuos vacunados no logran desarrollar anticuerpos frente a la enfermedad y por lo tanto, podrían resultar infectados al contactar con individuos enfermos...Fac. de Estudios EstadísticosTRUEunpu

Trends in Infectious Diseases

This book gives a comprehensive overview of recent trends in infectious diseases, as well as general concepts of infections, immunopathology, diagnosis, treatment, epidemiology and etiology to current clinical recommendations in management of infectious diseases, highlighting the ongoing issues, recent advances, with future directions in diagnostic approaches and therapeutic strategies. The book focuses on various aspects and properties of infectious diseases whose deep understanding is very important for safeguarding human race from more loss of resources and economies due to pathogens

Essays on the Economics of Vaccination

I examine vaccination behavior during a measles outbreak. By abandoning the rationalexpectations framework, I develop a model of vaccine behavior which recreates empirically observed vaccine hesitancy, as well as vaccination spikes during an outbreak. I use an agent-based model to simulate disease spread and agent behavior in a measles outbreak, in which rational agents minimize their expected costs by choosing their vaccination state. I allow some agents to instead use a heuristic, and others to have misinformation regarding vaccine risks, and finds that both reduce welfare. Including a social network has an ambiguous effect, as using more relevant local data allows agents to better estimate their risk from disease, but the same social network amplifies the impact of misinformation. I then examine a series of regulator interventions, and find that using a social media campaign to change agent’s perceptions of their peers’ views is the most cost-effective intervention. This presents regulators with a new framework with which to understand vaccine hesitancy, and an expanded menu of options to employ in the event of an outbreak

Coronaviruses Research in BRICS Countries

SARS-CoV-2 has infected more than 105 million people worldwide. During this pandemic, researchers and clinicians have been working to understand the molecular mechanisms that underpin viral pathogenesis by studying viral–host interactions. Now, with the global rollout of various COVID-19 vaccines—based on the neutralization of the spike protein using different technologies—viral immunology and cell-based immunity are being investigated. Researchers are also studying how various SARS-CoV-2 genetic mutations will impact the efficacy of these COVID-19 vaccines. At the same time, various antiviral drugs have been identified or repurposed that have potential as anti-SARS-CoV-2 treatments. BRICS (Brazil, Russia, India, China, and South Africa) is the acronym used to associate five major emerging national economies. The BRICS countries are known for their significant influence on regional affairs, including being leaders in scientific and clinical research and innovation. This Special Issue includes researchers from BRICS countries, in particular South Africa, involved in the study of SARS-CoV-2 and COVID-19. Original articles, as well as new perspectives or reviews on the matter, were welcomed. Research in the fields of vaccine studies, pathogenesis, genetic mutations, viral immunology, and antiviral drugs were especially encouraged

Optimization and control of virus-host systems

Optimization and control are powerful tools to design a system that works as effectively as possible. In this thesis, we focus on applications of model-based optimization and control in complex virus-host systems at multiple scales. Viruses that infect bacteria, i.e., bacteriophage or ‘phage’, are increasingly considered as treatment options for the control and clearance of bacterial infections, particularly as compassionate use therapy for multi-drug resistant infections. Here, we evaluate principles underlying why careful application of multiple phage (i.e., a ‘cocktail’) might lead to therapeutic success in contrast to the failure of single-strain phage therapy to control an infection. We combine dynamical modeling of phage, bacteria, and host immune cell populations with control-theoretic principles (via optimal control theory) to devise phage cocktails and delivery schedules to control the bacterial populations. However, a risk in using cocktails of different phage is that bacteria could simultaneously develop resistance to all injected phage (i.e., selecting for multi-phage resistant). The next step is to understand how to pre-select phage that have adapted via co-evolution with bacterial strains and then to efficiently use these ‘future’ phage to clear the infection early on. In doing so, we develop the evolutionarily robust phage therapy in immunodeficient hosts given the infection networks that was identified in co-evolutionary training. Optimization and control not only can be applied to bacteria-phage-immune systems (i.e., at the microbial level) to help design phage therapy, but also can be applied to epidemiological systems (i.e., at the large-scale population level) to guide the development and deployment of efficient interventions. Lockdowns and stay-at-home orders have reduced the transmission of SARS-CoV-2 but have come with significant social and economic costs. Here, we describe a control theory framework combining population-scale viral and serological testing as part of an individualized approach to control COVID-19 spread. The aim is to develop policies for modulating individualize contact rates depending on both personalized disease status and the status of the epidemic at the population scale. Altogether in this thesis, we apply control strategies to alleviate the burden or spread of disease at multiple scales.Ph.D

Mathematical models of RNA interference in plants

RNA interference (RNAi), or Post-Transcriptional Gene Silencing (PTGS), is a biological process which uses small RNAs to regulate gene expression on a cellular level, typically by causing the destruction of specfic mRNA molecules. This biological pathway is found in both plants and animals, and can be used\ud as an effective strategy in defending cells against parasitic nucleotide sequences, viruses and transposons. In the case of plants, it also constitutes a major component of the adaptive immune system. RNAi is characterised by the ability to induce sequence-specific degradation of target messenger RNA (mRNAs) and methylation of target gene sequences. The small interfering RNA produced within the initiated cell is not only used locally but can also be transported into neighbouring cells, thus acting as a mobile warning signal. In the first part of the thesis I develop and analyse a new mathematical model of the plant immune response to a viral infection, with particular emphasis on the role of RNA interference. The model explicitly includes two different time delays, one to represent the maturation period of undifferentiated cells, and another to account for the time required for the RNAi propagating signal to reach other parts of the plant, resulting in either recovery or warning of susceptible cells. Analytical and numerical bifurcation theory is used to identify parameter regions associated with recovery and resistant plant phenotypes, as well as possible chronic infections. The analysis shows that the maturation time plays an important role in determining the dynamics, and that long-term host recovery does not depend on the speed of the warning signal but rather on the strength of local recovery. At best, the warning signal can amplify and hasten recovery, but by itself it is not competent at eradicating the infection. In the second part of the thesis I derive and analyse a new mathematical model of plant viral co-infection with particular account for RNA-mediated cross-protection in a single plant host. The model exhibits four non-trivial steady states, i.e. a disease-free steady state, two one-virus endemic equilibria, and a co-infected steady state. I obtained the basic reproduction number for each of the two viral strains and performed extensive numerical bifurcation analysis to investigate the stability of all steady states and identified parameter regions where the system exhibits synergistic or antagonistic interactions between viral strains, as well as different types of host recovery. The results indicate that the propagating component of RNA interference plays a significant role in determining whether both viruses can persist simultaneously, and as such, it controls whether the plant is able to support some constant level of both infections. If the two viruses are sufficiently immunologically related, the least harmful of the two viruses becomes dominant, and the plant experiences cross-protection. In the third part of the thesis I investigate the properties of intracellular dynamics of RNA interference and its capacity as a gene regulator by extending a well known model of RNA interference with time delays. For each of the two amplification pathways of the model, I consider the cumulative effects of delay in dsRNA-primed synthesis associated with the non-instantaneous nature of chemical signals and component transportation delay. An extensive bifurcation analysis is performed to demonstrate the significance of different parameters, and to investigate how time delays can affect the bi-stable regime in the model