Mathematical Assessment of the Role of Early Latent Infections and Targeted Control Strategies on Syphilis Transmission Dynamics.

A new multi-stage deterministic model for the transmission dynamics of syphilis, which incorporates disease transmission by individuals in the early latent stage of syphilis infection and the reversions of early latent syphilis to the primary and secondary stages, is formulated and rigorously analysed. The model is used to assess the population-level impact of preventive (condom use) and therapeutic measures (treatment using antibiotics) against the spread of the disease in a community. It is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated control reproduction number (denoted by [Formula: see text]) is less than unity. A special case of the model is shown to have a unique and globally-asymptotically stable endemic equilibrium whenever the associated reproduction number (denoted by [Formula: see text]) exceeds unity. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to syphilis transmission dynamics in Nigeria, show that the top three parameters that drive the syphilis infection (with respect to [Formula: see text]) are the disease transmission rate ([Formula: see text]), compliance in condom use (c) and efficacy of condom ([Formula: see text]). Numerical simulations of the model show that the targeted treatment of secondary syphilis cases is more effective than the targeted treatment of individuals in the primary or early latent stage of syphilis infection.

Comments on "A Mathematical Study to Control Visceral Leishmaniasis: An Application to South Sudan".

Deterministic (ordinary differential equation) models for the transmission dynamics of vector-borne diseases that incorporate disease-induced death in the host(s) population(s) are generally known to exhibit the phenomenon of backward bifurcation (where a stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number of the model is less than unity). Further, it is well known that, in these models, the phenomenon of backward bifurcation does not occur when the disease-induced death rate is negligible (e.g., if the disease-induced death rate is set to zero). In a recent paper on the transmission dynamics of visceral leishmaniasis (a disease vectored by sandflies), titled "A Mathematical Study to Control Visceral Leishmaniasis: An Application to South Sudan," published in Bulletin of Mathematical Biology, Vol. 79, Pages 1110-1134, 2017, Ghosh et al. (2017) stated that their deterministic model undergoes a backward bifurcation even when the disease-induced mortality in the host population is set to zero. This result is contrary to the well-established theory on the dynamics of vector-borne diseases. In this short note, we illustrate some of the key errors in the Ghosh et al. (2017) study.

Medium-chain-length poly-3-hydroxyalkanoates-carbon nanotubes composite anode enhances the performance of microbial fuel cell.

Insufficient power generation from a microbial fuel cell (MFC) hampers its progress towards utility-scale development. Electrode modification with biopolymeric materials could potentially address this issue. In this study, medium-chain-length poly-3-hydroxyalkanoates (PHA)/carbon nanotubes (C) composite (CPHA) was successfully applied to modify the surface of carbon cloth (CC) anode in MFC. Characterization of the functional groups on the anodic surface and its morphology was carried out. The CC-CPHA composite anode recorded maximum power density of 254 mW/m2, which was 15-53% higher than the MFC operated with CC-C (214 mW/m2) and pristine CC (119 mW/m2) as the anode in a double-chambered MFC operated with Escherichia coli as the biocatalyst. Electrochemical impedance spectroscopy and cyclic voltammetry showed that power enhancement was attributed to better electron transfer capability by the bacteria for the MFC setup with CC-CPHA anode.

Mathematical analysis of a model for AVL-HIV co-endemicity.

A model for the transmission dynamics of Anthroponotic Visceral Leishmaniasis (AVL) and human immunodeficiency virus (HIV) in a population is developed and used to assess the impact of the spread of each disease on the overall transmission dynamics. As for other vector-borne disease models, the AVL component of the model undergoes backward bifurcation when the associated reproduction number of the AVL-only sub-model (denoted by RL) is less than unity. Uncertainty and sensitivity analyzes of the model, using data relevant to the dynamics of the two diseases in Ethiopia, show that the top three parameters that drive the AVL infection (with respect to the associated response function, RL) are the average number of times a sandfly bites humans per unit time (σV), carrying capacity of vectors (KV) and transmission probability from infected humans to susceptible sandflies (ß2). The distribution of RL is RL∈[0.06,3.94] with a mean of RL=1.08. Furthermore, the top three parameters that affect HIV dynamics (with respect to the response function RH) are the transmission rate of HIV (ßH), HIV-induced death rate (δH), and the modification parameter for the increase in infectiousness of AIDS individuals in comparison to HIV infected without clinical symptoms of AIDS (ωH). The distribution of RH is RH∈[0.88,2.79] with a mean of RH=1.46. The dominant parameters that affect the dynamics of the full VL-HIV model (with respect to the associated reproduction number, RLH, as the response function) are the transmission rate of HIV (ßH), the average number of times a sandfly bites humans per unit time (σV), and HIV-induced death rate (δH) (the distribution of RLH is RLH∈[0.88,3.94] with a mean of RLH=1.64). Numerical simulations of the model show that the two diseases co-exist (with AVL dominating, but not driving HIV to extinction) whenever the reproduction number of each disease exceeds unity. It is shown that AVL can invade a population at HIV-endemic state if a certain threshold quantity, known as invasion reproduction number, exceeds unity.

Differential characteristics of primary infection and re-infection can cause backward bifurcation in HCV transmission dynamics.

Backward bifurcation, a phenomenon typically characterized by the co-existence of multiple stable equilibria when the associated reproduction number of the model is less than unity, has been observed in numerous disease transmission models. This study establishes, for the first time, the presence of this phenomenon in the transmission dynamics of hepatitis C virus (HCV) within an IDU population. It is shown that the phenomenon does not exist under four scenarios, namely (i) in the absence of re-infection, (ii) in the absence of differential characteristics of HCV infection (with respect to infectivity, progression, treatment and recovery) between re-infected individuals and primary-infected individuals, (iii) when re-infected and treated individuals do not transmit HCV infection and (iv) when the average infectivity-adjusted duration of re-infection is less than that of primary infection. This study identifies, using sensitivity analysis, five parameters of the model that have the most influence on the disease transmission dynamics, namely: effective contact rate, progression rate from acute to chronic infection, recovery rate from acute infection, natural death rate and the relative infectiousness of chronically-infected individuals. Numerical simulations of the model show that the re-infection of recovered individuals has marginal effect on the HCV burden (as measured in terms of the cumulative incidence and the prevalence of the disease) in the IDU community. Furthermore, treatment of infected IDUs, even for small rate (such as 4%), offers significant impact on curtailing HCV spread in the community.

Growth kinetics, effect of carbon substrate in biosynthesis of mcl-PHA by Pseudomonas putida Bet001.

Growth associated biosynthesis of medium chain length poly-3-hydroxyalkanoates (mcl-PHA) in Pseudomonas putida Bet001 isolated from palm oil mill effluent was studied. Models with substrate inhibition terms described well the kinetics of its growth. Selected fatty acids (C8:0 to C18:1) and ammonium were used as carbon and nitrogen sources during growth and PHA biosynthesis, resulting in PHA accumulation of about 50 to 69% (w/w) and PHA yields ranging from 10.12 g L(-1) to 15.45 g L(-1), respectively. The monomer composition of the PHA ranges from C4 to C14, and was strongly influenced by the type of carbon substrate fed. Interestingly, an odd carbon chain length (C7) monomer was also detected when C18:1 was fed. Polymer showed melting temperature (T m) of 42.0 (± 0.2) °C, glass transition temperature (T g) of -1.0 (± 0.2) °C and endothermic melting enthalpy of fusion (ΔHf) of 110.3 (± 0.1) J g(-1). The molecular weight (M w) range of the polymer was relatively narrow between 55 to 77 kDa.

Dynamics of Mycobacterium and bovine tuberculosis in a human-buffalo population.

A new model for the transmission dynamics of Mycobacterium tuberculosis and bovine tuberculosis in a community, consisting of humans and African buffalos, is presented. The buffalo-only component of the model exhibits the phenomenon of backward bifurcation, which arises due to the reinfection of exposed and recovered buffalos, when the associated reproduction number is less than unity. This model has a unique endemic equilibrium, which is globally asymptotically stable for a special case, when the reproduction number exceeds unity. Uncertainty and sensitivity analyses, using data relevant to the dynamics of the two diseases in the Kruger National Park, show that the distribution of the associated reproduction number is less than unity (hence, the diseases would not persist in the community). Crucial parameters that influence the dynamics of the two diseases are also identified. Both the buffalo-only and the buffalo-human model exhibit the same qualitative dynamics with respect to the local and global asymptotic stability of their respective disease-free equilibrium, as well as with respect to the backward bifurcation phenomenon. Numerical simulations of the buffalo-human model show that the cumulative number of Mycobacterium tuberculosis cases in humans (buffalos) decreases with increasing number of bovine tuberculosis infections in humans (buffalo).

Growth kinetics, effect of carbon substrate in biosynthesis of mcl-PHA by Pseudomonas putida Bet001

Growth associated biosynthesis of medium chain length poly-3-hydroxyalkanoates (mcl-PHA) in Pseudomonas putida Bet001 isolated from palm oil mill effluent was studied. Models with substrate inhibition terms described well the kinetics of its growth. Selected fatty acids (C8:0 to C18:1) and ammonium were used as carbon and nitrogen sources during growth and PHA biosynthesis, resulting in PHA accumulation of about 50 to 69% (w/w) and PHA yields ranging from 10.12 g L-1 to 15.45 g L-1, respectively. The monomer composition of the PHA ranges from C4 to C14, and was strongly influenced by the type of carbon substrate fed. Interestingly, an odd carbon chain length (C7) monomer was also detected when C18:1 was fed. Polymer showed melting temperature (Tm) of 42.0 (± 0.2) °C, glass transition temperature (Tg) of -1.0 (± 0.2) °C and endothermic melting enthalpy of fusion (ΔHf) of 110.3 (± 0.1) J g-1. The molecular weight (Mw) range of the polymer was relatively narrow between 55 to 77 kDa.

Emergency department and 'Google flu trends' data as syndromic surveillance indicators for seasonal influenza.

We evaluated syndromic indicators of influenza disease activity developed using emergency department (ED) data - total ED visits attributed to influenza-like illness (ILI) ('ED ILI volume') and percentage of visits attributed to ILI ('ED ILI percent') - and Google flu trends (GFT) data (ILI cases/100 000 physician visits). Congruity and correlation among these indicators and between these indicators and weekly count of laboratory-confirmed influenza in Manitoba was assessed graphically using linear regression models. Both ED and GFT data performed well as syndromic indicators of influenza activity, and were highly correlated with each other in real time. The strongest correlations between virological data and ED ILI volume and ED ILI percent, respectively, were 0·77 and 0·71. The strongest correlation of GFT was 0·74. Seasonal influenza activity may be effectively monitored using ED and GFT data.

Qualitative dynamics of lowly- and highly-pathogenic avian influenza strains.

A new deterministic model for the transmission dynamics of the lowly- and highly-pathogenic avian influenza (LPAI and HPAI) strains is designed and rigorously analyzed. The model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. It is shown that the re-infection of birds infected with the LPAI strain causes the backward bifurcation phenomenon. In the absence of such re-infection, the disease-free equilibrium of the model is globally-asymptotically stable when the associated reproduction number is less than unity. Using non-linear Lyapunov functions of Goh-Volterra type, the LPAI-only and HPAI-only boundary equilibria of the model are shown to be globally-asymptotically stable when they exist. A special case of the model is shown to have a continuum of co-existence equilibria whenever the associated reproduction numbers of the two strains are equal and exceed unity. Furthermore, numerical simulations of the model suggest that co-existence or competitive exclusion of the two strains can occur when the respective reproduction numbers of the two strains exceed unity.

Enzymatic synthesis of 6-O-glucosyl-poly(3-hydroxyalkanoate) in organic solvents and their binary mixture.

The effects of organic solvents and their binary mixture in the glucose functionalization of bacterial poly-3-hydroxyalkanoates catalyzed by Lecitase™ Ultra were studied. Equal volume binary mixture of DMSO and chloroform with moderate polarity was more effective for the enzyme catalyzed synthesis of the carbohydrate polymer at ≈38.2 (±0.8)% reactant conversion as compared to the mono-phasic and other binary solvents studied. The apparent reaction rate constant as a function of medium water activity (aw) was observed to increase with increasing solvent polarity, with optimum aw of 0.2, 0.4 and 0.7 (±0.1) observed in hydrophilic DMSO, binary mixture DMSO:isooctane and hydrophobic isooctane, respectively. Molecular sieve loading between 13 to 15gL(-1) (±0.2) and reaction temperature between 40 to 50°C were found optimal. Functionalized PHA polymer showed potential characteristics and biodegradability.

Lipase catalyzed ultrasonic synthesis of poly-4-hydroxybutyrate-co-6-hydroxyhexanoate.

Four different lipases were compared for ultrasound-mediated synthesis of the biodegradable copolymer poly-4-hydroxybutyrate-co-6-hydroxyhexanoate. The copolymerization was carried out in chloroform. Of the enzymes tested, Novozym 435 exhibited the highest copolymerization rate, in fact the reaction rate was observed to increase with about 26-fold from 30 to 50°C (7.9×10(-3)Ms(-1)), sonic power intensity of 2.6×10(3)Wm(-2) and dissipated energy of 130.4Jml(-1). Copolymerization rates with the Candida antarctica lipase A, Candida rugosa lipase, and Lecitase Ultra™ were lower at 2.4×10(-4), 1.3×10(-4) and 3.5×10(-4)Ms(-1), respectively. The catalytic efficiency depended on the enzyme. The efficiency ranged from 4.15×10(-3)s(-1)M(-1) for Novozym 435-1.48×10(-3)s(-1)M(-1) for C. rugosa lipase. Depending on the enzyme and sonication intensity, the monomer conversion ranged from 8.2% to 48.5%. The sonication power, time and temperature were found to affect the rate of copolymerization. Increasing sonication power intensity from 1.9×10(3) to 4.5×10(3)Wm(-2) resulted in an increased in acoustic pressure (P(a)) from 3.7×10(8) to 5.7×10(8)Nm(-2) almost 2.4-3.7 times greater than the acoustic pressure (1.5×10(8)Nm(-2)) that is required to cause cavitation in water. A corresponding acoustic particle acceleration (a) of 9.6×10(3)-1.5×10(4)ms(-2) was calculated i.e. approximately 984-1500 times greater than under the action of gravity.

Ultrasound assisted lipase catalyzed synthesis of poly-6-hydroxyhexanoate.

Ultrasonic irradiation greatly improved the Candida antarctica lipase B mediated ring opening polymerization of ε-caprolactone to poly-6-hydroxyhexanoate in the ionic liquid 1-ethyl-3-methylimidazolium tetraflouroborate. Compared to the conventional nonsonicated reaction, sonication improved the monomer conversion by 63% and afforded a polymer product of a narrower molecular weight distribution and a higher degree of crystallinity. Under sonication, the polydispersity index of the product was ~1.44 compared to a value of ~2.55 for the product of the conventional reaction. With sonication, nearly 75% of the monomer was converted to product, but the conversion was only ~16% for the reaction carried out conventionally. Compared to conventional operation, sonication enhanced the rate of polymer propagation by >2-fold and the turnover number of the lipase by >3-fold.

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.

Mathematical Analysis of a Model for Assessing the Impact of Antiretroviral Therapy, Voluntary Testing and Condom Use in Curtailing the Spread of HIV.

This paper presents a deterministic model for evaluating the impact of anti-retroviral drugs (ARVs), voluntary testing (using standard antibody-based and a DNA-based testing methods) and condom use on the transmission dynamics of HIV in a community. Rigorous qualitative analysis of the model show that it has a globally-stable disease-free equilibrium whenever a certain epidemiological threshold, known as the effective reproduction number , is less than unity. The model has an endemic equilibrium whenever . The endemic equilibrium is shown to be locally-asymptotically stable for a special case. Numerical simulations of the model show that the use of the combined testing and treatment strategy is more effective than the use of the standard ELISA testing method with ARV treatment, even for the use of condoms as a singular strategy. Furthermore, the universal strategy (which involves the use of condoms, the two testing methods and ARV treatment) is always more effective than the combined use of the standard ELISA testing method and ARVs.

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.

Qualitative assessment of the role of public health education program on HIV transmission dynamics.

This paper presents a non-linear deterministic model for assessing the impact of public health education campaign on curtailing the spread of the human immunodeficiency virus (HIV) pandemic in a population. Rigorous qualitative analysis of the model reveals that it exhibits the phenomenon of backward bifurcation (BB), where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the 'effective reproduction number' ('Reff), is less than unity. The epidemiological implication of BB is that a public health education campaign could fail to effectively control HIV even when the classical requirement of having the associated reproduction number less than unity is satisfied. Furthermore, an explicit threshold value is derived above which such an education campaign could lead to detrimental outcome (increase disease burden) and below which it would have positive population-level impact (reduce disease burden in the community). It is shown that the BB phenomenon is caused by imperfect efficacy of the public health education program. The model is used to assess the potential impact of some targeted public health education campaigns using data from numerous countries.

Incremental role of male circumcision on a generalised HIV epidemic through its protective effect against other sexually transmitted infections: from efficacy to effectiveness to population-level impact.

BACKGROUND: Male circumcision (MC) can reduce HIV acquisition. However, a better understanding of the indirect protective effect of MC on sexually transmitted infections (STIs) is required. OBJECTIVE: To assess the incremental benefits conferred by MC on HIV infection at the individual level in circumcision trials (no herd immunity effect) and at the population level (with herd immunity effect) owing to its protective effect against other STIs. METHODS: A dynamic stochastic model of HIV and STI infections in a Kenyan population was used to simulate the impact of MC offered to a few trial participants or to a large proportion of men in order to study the protective role of MC on HIV infection at the individual and population levels. RESULTS: Fewer than 20% of the HIV infections prevented in the circumcised arm of the circumcision trials (individual level) could be attributable to the efficacy of MC against STIs rather than against HIV. At the population level, MC can significantly reduce the prevalence of HIV, especially among men and women in the longer term. However, even at the population level, the long-term incremental impact of MC on HIV due to the protection against STI is modest (even if MC efficacy against the STI and STI prevalence was high). CONCLUSIONS: The protection of MC against STI contributes little to the overall effect of MC on HIV. Additional work is needed to determine whether, and under what conditions, the protective effect of MC efficacy against STIs can have a significant incremental benefit on the HIV epidemic.

Protecting residential care facilities from pandemic influenza.

It is widely believed that protecting health care facilities against outbreaks of pandemic influenza requires pharmaceutical resources such as antivirals and vaccines. However, early in a pandemic, vaccines will not likely be available and antivirals will probably be of limited supply. The containment of pandemic influenza within acute-care hospitals anywhere is problematic because of open connections with communities. However, other health care institutions, especially those providing care for the disabled, can potentially control community access. We modeled a residential care facility by using a stochastic compartmental model to address the question of whether conditions exist under which nonpharmaceutical interventions (NPIs) alone might prevent the introduction of a pandemic virus. The model projected that with currently recommended staff-visitor interactions and social distancing practices, virus introductions are inevitable in all pandemics, accompanied by rapid internal propagation. The model identified staff reentry as the critical pathway of contagion, and provided estimates of the reduction in risk required to minimize the probability of a virus introduction. By using information on latency for historical and candidate pandemic viruses, we developed NPIs that simulated notions of protective isolation for staff away from the facility that reduced the probability of bringing the pandemic infection back to the facility to levels providing protection over a large range of projected pandemic severities. The proposed form of protective isolation was evaluated for social plausibility by collaborators who operate residential facilities. It appears unavoidable that NPI combinations effective against pandemics more severe than mild imply social disruption that increases with severity.

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.