Role of incidence function in vaccine-induced backward bifurcation in some HIV models

The phenomenon of backward bifurcation in disease models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction number is less than unity, has important implications for disease control. In such a scenario, the classical requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, condition for disease elimination. This paper addresses the role of the choice of incidence function in a vaccine-induced backward bifurcation in HIV models. Several examples are given where backward bifurcations occur using standard incidence, but not with their equivalents that employ mass action incidence. Furthermore, this result is independent of the type of vaccination program adopted. These results emphasize the need for further work on the incidence functions used in HIV models.     

Modelling the Transmission Dynamics and Control of the Novel 2009 Swine Influenza (H1N1) Pandemic

The paper presents a deterministic compartmental model for the transmission dynamics of swine influenza (H1N1) pandemic in a population in the presence of an imperfect vaccine and use of drug therapy for confirmed cases. Rigorous analysis of the model, which stratifies the infected population in terms of their risk of developing severe illness, reveals that it exhibits a vaccine-induced backward bifurcation when the associated reproduction number is less than unity. The epidemiological consequence of this result is that the effective control of H1N1, when the reproduction number is less than unity, in the population would then be dependent on the initial sizes of the subpopulations of the model. For the case where the vaccine is perfect, it is shown that having the reproduction number less than unity is necessary and sufficient for effective control of H1N1 in the population (in such a case, the associated disease-free equilibrium is globally asymptotically stable). The model has a unique endemic equilibrium when the reproduction number exceeds unity. Numerical simulations of the model, using data relevant to the province of Manitoba, Canada, show that it reasonably mimics the observed H1N1 pandemic data for Manitoba during the first (Spring) wave of the pandemic. Further, it is shown that the timely implementation of a mass vaccination program together with the size of the Manitoban population that have preexisting infection-acquired immunity (from the first wave) are crucial to the magnitude of the expected burden of disease associated with the second wave of the H1N1 pandemic. With an estimated vaccine efficacy of approximately 80%, it is projected that at least 60% of Manitobans need to be vaccinated in order for the effective control or elimination of the H1N1 pandemic in the province to be feasible. Finally, it is shown that the burden of the second wave of H1N1 is expected to be at least three times that of the first wave, and that the second wave would last until the end of January or early February, 2010.     

Modelling strategies for controlling SARS outbreaks

Severe acute respiratory syndrome (SARS), a new, highly contagious, viral disease, emerged in China late in 2002 and quickly spread to 32 countries and regions causing in excess of 774 deaths and 8098 infections worldwide. In the absence of a rapid diagnostic test, therapy or vaccine, isolation of individuals diagnosed with SARS and quarantine of individuals feared exposed to SARS virus were used to control the spread of infection. We examine mathematically the impact of isolation and quarantine on the control of SARS during the outbreaks in Toronto, Hong Kong, Singapore and Beijing using a deterministic model that closely mimics the data for cumulative infected cases and SARS-related deaths in the first three regions but not in Beijing until mid-April, when China started to report data more accurately. The results reveal that achieving a reduction in the contact rate between susceptible and diseased individuals by isolating the latter is a critically important strategy that can control SARS outbreaks with or without quarantine. An optimal isolation programme entails timely implementation under stringent hygienic precautions defined by a critical threshold value. Values below this threshold lead to control, but those above are associated with the incidence of new community outbreaks or nosocomial infections, a known cause for the spread of SARS in each region. Allocation of resources to implement optimal isolation is more effective than to implement sub-optimal isolation and quarantine together. A community-wide eradication of SARS is feasible if optimal isolation is combined with a highly effective screening programme at the points of entry.     

Long-lasting insecticidal nets and the quest for malaria eradication: a mathematical modeling approach

Journal of Mathematical Biology - Recent dramatic declines in global malaria burden and mortality can be largely attributed to the large-scale deployment of insecticidal-based measures, namely...     

Biosynthesis and Characterization of Polyhydroxyalkanoates Copolymers Produced by Pseudomonas putida Bet001 Isolated from Palm Oil Mill Effluent

The biosynthesis and characterization of medium chain length poly-3-hydroxyalkanoates (mcl-PHA) produced by Pseudomonas putida Bet001 isolated from palm oil mill effluent was studied. The biosynthesis of mcl-PHA in this newly isolated microorganism follows a growth-associated trend. Mcl-PHA accumulation ranging from 49.7 to 68.9% on cell dry weight (CDW) basis were observed when fatty acids ranging from octanoic acid (C_8∶0) to oleic acid (C_18∶1) were used as sole carbon and energy source. Molecular weight of the polymer was found to be ranging from 55.7 to 77.7 kDa. Depending on the type of fatty acid used, the ¹H NMR and GCMSMS analyses of the chiral polymer showed a composition of even and odd carbon atom chain with monomer length of C4 to C14 with C8 and C10 as the principal monomers. No unsaturated monomer was detected. Thermo-chemical analyses showed the accumulated PHA to be semi-crystalline polymer with good thermal stability, having a thermal degradation temperature (T _d) of 264.6 to 318.8 (±0.2) ^oC, melting temperature (T _m) of 43. (±0.2) ^oC, glass transition temperature (T _g) of −1.0 (±0.2) ^oC and apparent melting enthalpy of fusion (ΔH _f) of 100.9 (±0.1) J g⁻¹.     

Dynamics Analysis of a Multi-strain Cholera Model with an Imperfect Vaccine

A new two-strain model, for assessing the impact of basic control measures, treatment and dose-structured mass vaccination on cholera transmission dynamics in a population, is designed. The model has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. The model has a unique, and locally-asymptotically stable, endemic equilibrium when the threshold quantity exceeds unity and another condition holds. Numerical simulations of the model show that, with the expected 50 % minimum efficacy of the first vaccine dose, vaccinating 55 % of the susceptible population with the first vaccine dose will be sufficient to effectively control the spread of cholera in the community. Such effective control can also be achieved if 50 % of the first vaccine dose recipients take the second dose. It is shown that a control strategy that emphasizes the use of antibiotic treatment is more effective than one that emphasizes the use of basic (non-pharmaceutical) anti-cholera control measures only. Numerical simulations show that, while the universal strategy (involving all three control measures) gives the best outcome in minimizing cholera burden in the community, the combined basic anti-cholera control measures and treatment strategy also has very effective community-wide impact.     

Backward bifurcations in dengue transmission dynamics

A deterministic model for the transmission dynamics of a strain of dengue disease, which allows transmission by exposed humans and mosquitoes, is developed and rigorously analysed. The model, consisting of seven mutually-exclusive compartments representing the human and vector dynamics, has a locally-asymptotically stable disease-free equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number(R(0)) is less than unity. Further, the model exhibits the phenomenon of backward bifurcation, where the stable DFE coexists with a stable endemic equilibrium. The epidemiological consequence of this phenomenon is that the classical epidemiological requirement of making R(0) less than unity is no longer sufficient, although necessary, for effectively controlling the spread of dengue in a community. The model is extended to incorporate an imperfect vaccine against the strain of dengue. Using the theory of centre manifold, the extended model is also shown to undergo backward bifurcation. In both the original and the extended models, it is shown, using Lyapunov function theory and LaSalle Invariance Principle, that the backward bifurcation phenomenon can be removed by substituting the associated standard incidence function with a mass action incidence. In other words, in addition to establishing the presence of backward bifurcation in models of dengue transmission, this study shows that the use of standard incidence in modelling dengue disease causes the backward bifurcation phenomenon of dengue disease.     

Climate,environmental and socio-economic change: weighing up the balance in vector-borne disease transmission

Arguably one of the most important effects of climate change is the potential impact on human health. While this is likely to take many forms, the implications for future transmission of vector-borne diseases (VBDs), given their ongoing contribution to global disease burden, are both extremely important and highly uncertain. In part, this is owing not only to data limitations and methodological challenges when integrating climate-driven VBD models and climate change projections, but also, perhaps most crucially, to the multitude of epidemiological, ecological and socio-economic factors that drive VBD transmission, and this complexity has generated considerable debate over the past 10–15 years. In this review, we seek to elucidate current knowledge around this topic, identify key themes and uncertainties, evaluate ongoing challenges and open research questions and, crucially, offer some solutions for the field. Although many of these challenges are ubiquitous across multiple VBDs, more specific issues also arise in different vector–pathogen systems.     

Thermo-kinetics of lipase-catalyzed synthesis of 6-O-glucosyldecanoate

Lipase-catalyzed synthesis of 6-O-glucosyldecanoate from d-glucose and decanoic acid was performed in dimethyl sulfoxide (DMSO), a mixture of DMSO and tert-butanol and tert-butanol alone with a decreasing order of polarity. The highest conversion yield (> 65%) of decanoic acid was obtained in the blended solvent of intermediate polarity mainly because it could dissolve relatively large amounts of both the reactants. The reaction obeyed Michaelis-Menten type of kinetics. The affinity of the enzyme towards the limiting substrate (decanoic acid) was not affected by the polarity of the solvent, but increased significantly with temperature. The esterification reaction was endothermic with activation energy in the range of 60-67 kJ mol?1. Based on the Gibbs energy values, in the solvent blend of DMSO and tert-butanol the position of the equilibrium was shifted more towards the products compared to the position in pure solvents. Monoester of glucose was the main product of the reaction.