(R1412) Stability and Bifurcation of a Cholera Epidemic Model with Saturated Recovery Rate

In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound matrix are used to study the global stability of the system. The conditions that guarantee the occurrence of local bifurcation and backward bifurcation are determined. Finally, numerical simulation is used to investigate the global dynamical behavior of the Cholera epidemic model and understand the effects of parameters on evolution of the disease in the environment. It is observed that the solution of the model is very sensitive to varying in parameters values and different types of bifurcations are obtained including backward bifurcation

Extinction of cholera using deterministic and stochastic models incorporating vigilant human compartment

We study the effect of vaccination, sanitation and public health sensitization as prevention and control measures of cholera in deterministic and stochastic frameworks. To achieve this, a deterministic mathematical model incorporating the class of vigilant individuals is proposed and analyzed. The results from the stability analysis show that the disease-free equilibrium solution is globally asymptotically stable if R0 < 1. The model is then extended to incorporate random effect using the method of transition probabilities. Numerically, we approximate the expected extinction time of the disease if certain conditions are satisfied. As Vibrio cholerae multiplies at a fast rate in the environment, it is recommended that regular disinfection of the affected areas as well as public health sensitization be done.Publisher's Versio

Optimal control approaches for combining medicines and mosquito control in tackling dengue

Dengue is a debilitating and devastating viral infection spread by mosquito vectors, and over half the world’s population currently live at risk of dengue (and other flavivirus) infections. Here we use an integrated epidemiological and vector ecology framework to predict optimal approaches for tackling dengue. Our aim is to investigate how vector control and/or vaccination strategies can be best combined and implemented for dengue disease control on small networks, and whether these optimal strategies differ under different circumstances. We show that a combination of vaccination programmes and the release of genetically modified self-limiting mosquitoes (comparable to sterile insect approaches) is always considered the most beneficial strategy for reducing the number of infected individuals, due to both methods having differing impacts on the underlying disease dynamics. Additionally, depending on the impact of human movement on the disease dynamics, the optimal way to combat the spread of dengue is to focus prevention efforts on large population centres. Using mathematical frameworks, such as optimal control, are essential in developing predictive management and mitigation strategies for dengue disease control

Use of a Cholera Rapid Diagnostic Test during a Mass Vaccination Campaign in Response to an Epidemic in Guinea, 2012

During the 2012 cholera outbreak in the Republic of Guinea, the Ministry of Health, supported by Médecins Sans Frontières - Operational Center Geneva, used the oral cholera vaccine Shanchol as a part of the emergency response. The rapid diagnostic test (RDT) Crystal VC, widely used during outbreaks, detects lipopolysaccharide antigens of Vibrio cholerae O1 and O139, both included in Shanchol. In the context of reactive use of a whole-cell cholera vaccine in a region where cholera cases have been reported, it is essential to know what proportion of vaccinated individuals would be reactive to the RDT and for how long after vaccination

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

The Public Funding of Health Care: A Brief Historical Overview of Principles, Practices, and Motives

Nationally sponsored programs designed to fund health care for the general public are largely a twentieth century phenomenon. Yet a long glance backward at the medical and public health history of Western civilization, extending from the ancient Greeks to the twentieth century, reveals earlier periods when governments, religious institutions, and other groups provided some measure of medical relief for the sick, the poor, and the homeless. In this essay, I will provide not an exhaustive but rather an illustrative account of this oft forgotten fact. My objectives are threefold. First, to remind us that the active concern of society for the health of its citizens is hardly a new development arising full born, as it were, out of the biomedical revolution and refined moral sensibilities of our present age. As I will suggest, our current interest in public health, and the related question of how to allocate medical resources fairly, is part of a larger evolutionary social process. Second, to conjecture that the impulse of caring for the sick and injured, using public or private resources,1 is typically driven by a variety of sometimes overlapping motivations, both religious and secular in origin. Third, to indicate that no single monolithic philosophy of providing medical care for the masses emerges from the historical record. That is, no unified pattern of health care organization or individual or communal motivation can plausibly account for this seemingly altruistic behavior, behavior which is putatively aimed at promoting the common good of all members of society. Given the interdisciplinary scope of this discussion, my inquiry will weave together sociological, psychological, and philosophical strands of evidence. Constraints of length will limit us primarily to developments in Europe and the United States. In the end, a limited sampling of societal practices, individual or communal motivations, and philosophical considerations will indicate that no simple story can be told about the public or private funding of health care. Proceeding more or less chronologically, I will introduce evidence demonstrating that redemptive, utilitarian, prudential, and charitable impulses (among others) are at work in the humane decision to use public or private funds to provide medical care for the benefit of the sick or infirm. While I do not claim that these four motivations constitute a complete list, they do emerge as a recurring and significant typology — helping to solidify the emerging modern public health movement in England, the United States, and elsewhere in the West by the late nineteenth century

Seroconversion and Kinetics of Vibriocidal Antibodies during the First 90 Days of Re-Vaccination with Oral Cholera Vaccine in an Endemic Population

Despite the successful introduction of oral cholera vaccines, Zambia continues to experience multiple, sporadic, and protracted cholera outbreaks in various parts of the country. While vaccines have been useful in staying the cholera outbreaks, the ideal window for re-vaccinating individuals resident in cholera hotspot areas remains unclear. Using a prospective cohort study design, 225 individuals were enrolled and re-vaccinated with two doses of Shanchol™, regardless of previous vaccination, and followed-up for 90 days. Bloods were collected at baseline before re-vaccination, at day 14 prior to second dosing, and subsequently on days 28, 60, and 90. Vibriocidal assay was performed on samples collected at all five time points. Our results showed that anti-LPS and vibriocidal antibody titers increased at day 14 after re-vaccination and decreased gradually at 28, 60, and 90 days across all the groups. Seroconversion rates were generally comparable in all treatment arms. We therefore conclude that vibriocidal antibody titers generated in response to re-vaccination still wane quickly, irrespective of previous vaccination status. However, despite the observed decline, the levels of vibriocidal antibodies remained elevated over baseline values across all groups, an important aspect for Zambia where there is no empirical evidence as to the ideal time for re-vaccination

Simulations for designing and interpreting intervention trials in infectious diseases.

BACKGROUND: Interventions in infectious diseases can have both direct effects on individuals who receive the intervention as well as indirect effects in the population. In addition, intervention combinations can have complex interactions at the population level, which are often difficult to adequately assess with standard study designs and analytical methods. DISCUSSION: Herein, we urge the adoption of a new paradigm for the design and interpretation of intervention trials in infectious diseases, particularly with regard to emerging infectious diseases, one that more accurately reflects the dynamics of the transmission process. In an increasingly complex world, simulations can explicitly represent transmission dynamics, which are critical for proper trial design and interpretation. Certain ethical aspects of a trial can also be quantified using simulations. Further, after a trial has been conducted, simulations can be used to explore the possible explanations for the observed effects. CONCLUSION: Much is to be gained through a multidisciplinary approach that builds collaborations among experts in infectious disease dynamics, epidemiology, statistical science, economics, simulation methods, and the conduct of clinical trials