Mathematical Biosciences and Engineering: latest papers Latest articles for selected journal The interplay between models and public health policies: Regional control for a class of spatially structured epidemics <em>(think globally, act locally)</em> Vincenzo Capasso and Sebastian Aniţa Thu, 1 Feb 2018 20:00:00 GMT Modeling ebola virus disease transmissions with reservoir in a complex virus life ecology 1$. The role of a contaminated environment is assessed by comparing the human infected component for the sub-model without the environment with that of the full model. Similarly, the sub-model without animals on the one hand and the sub-model without bats on the other hand are studied. It is shown that bats influence more the dynamics of EVD than the animals. Global sensitivity analysis shows that the effective contact rate between humans and fruit bats and the mortality rate for bats are the most influential parameters on the latent and infected human individuals. Numerical simulations, apart from supporting the theoretical results and the existence of a unique globally asymptotically stable endemic equilibrium for the full model, suggest further that: (1) fruit bats are more important in the transmission processes and the endemicity level of EVD than animals. This is in line with biological findings which identified bats as reservoir of Ebola viruses; (2) the indirect environmental contamination is detrimental to human beings, while it is almost insignificant for the transmission in bats. ]]> Tsanou Berge, Samuel Bowong, Jean Lubuma and Martin Luther Mann Manyombe Thu, 1 Feb 2018 20:00:00 GMT Mathematical analysis of a weather-driven model for the population ecology of mosquitoes vectorial reproduction number $({\mathcal R}_0)$ is less than unity. In the absence of density-dependence mortality in the larval stage, the autonomous version of the model has a unique and globally-asymptotically stable non-trivial equilibrium whenever $1<{\mathcal R}_0<{\mathcal R}_0^C$ (this equilibrium bifurcates into a limit cycle, via a Hopf bifurcation at ${\mathcal R}_0={\mathcal R}_0^C$). Numerical simulations of the weather-driven model, using temperature and rainfall data from three cities in Sub-Saharan Africa (Kwazulu Natal, South Africa; Lagos, Nigeria; and Nairobi, Kenya), show peak mosquito abundance occurring in the cities when the mean monthly temperature and rainfall values lie in the ranges $[22 - 25]^{0}$C, $[98 - 121]$ mm; $[24 - 27]^{0}$C, $[113 - 255]$ mm and $[20.5 - 21.5]^{0}$C, $[70 - 120]$ mm, respectively (thus, mosquito control efforts should be intensified in these cities during the periods when the respective suitable weather ranges are recorded). ]]> Kamaldeen Okuneye, Ahmed Abdelrazec and Abba B. Gumel Thu, 1 Feb 2018 20:00:00 GMT Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents Bull. Math. Biol. 68 (2006), 511--524]. Both subpopulations are assumed to differ in their movement with respect to local variations in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a non-local convolution of density values as proposed, in another context, in [R.M. Colombo and E. Rossi, Commun. Math. Sci., 13 (2015), 369--400]. An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. The numerical results demonstrate significant differences in the spatio-temporal behavior predicted by the different models, which suggest future research directions. ]]> Raimund Bürger, Gerardo Chowell, Elvis Gavilán, Pep Mulet and Luis M. Villada Thu, 1 Feb 2018 20:00:00 GMT Sex-biased prevalence in infections with heterosexual, direct, and vector-mediated transmission: A theoretical analysis     The third model considers vector-borne, instead of direct transmission. In this case, we were not able to find an analytical expression for the final attack ratios, but used instead numerical simulations. The results on final attack ratios are actually quite similar to those obtained with the second model. It is interesting to note that transient patterns can differ from final attack ratios, as new cases will tend to occur more often in the more susceptible sex, while later depletion of susceptibles may bias the ratio in the opposite direction.
   The analysis of these simple models, despite their lack of realism, can help in providing insight into, and assessment of, the potential role of gender-specific transmission in infections with multiple modes of transmission, such as Zika virus (ZIKV), by gauging what can be expected to be seen from epidemiological reports of new cases, disease incidence and seroprevalence surveys. ]]>
Andrea Pugliese, Abba B. Gumel, Fabio A. Milner and Jorge X. Velasco-Hernandez Thu, 1 Feb 2018 20:00:00 GMT On the usefulness of set-membership estimation in the epidemiology of infectious diseases Andreas Widder Thu, 1 Feb 2018 20:00:00 GMT An exact approach to calibrating infectious disease models to surveillance data: The case of HIV and HSV-2     In this work, we describe a general approach to calibrating infectious disease models to surveillance data. The technique is able to match surveillance data to high accuracy in a very efficient manner as it is based on the Newton-Raphson method for solving nonlinear systems. To demonstrate its robustness, we use the calibration technique on multiple models for the interacting dynamics of HIV and HSV-2. ]]> David J. Gerberry Thu, 1 Feb 2018 20:00:00 GMT A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment Federico Papa, Francesca Binda, Giovanni Felici, Marco Franzetti, Alberto Gandolfi, Carmela Sinisgalli and Claudia Balotta Thu, 1 Feb 2018 20:00:00 GMT Prediction of influenza peaks in Russian cities: Comparing the accuracy of two SEIR models Vasiliy N. Leonenko and Sergey V. Ivanov Thu, 1 Feb 2018 20:00:00 GMT A TB model: Is disease eradication possible in India?     Nowadays, incidence estimation relies increasingly more on notifications of new cases from routine surveillance. There is an urgent need for better estimates of the load of TB, in high-burden settings. We developed a simple model of TB transmission dynamics, using a dynamical system model, consisting of six classes of individuals. It contains the current medical epidemiologists' understanding of the spread of the Mycobacterium tuberculosis in humans, which is substantiated by field observations at the district level in India. The model incorporates the treatment options provided by the public and private sectors in India. Mathematically, an interesting feature of the system is that it exhibits a backward, or subcritical, bifurcation.
    One of the results of the investigation shows that the discrepancy between the diagnosis rates of the public and private sector does not seem to be the cause of the endemicity of the disease, and, unfortunately, even if they reached 100% of correct diagnosis, this would not be enough to achieve disease eradication.
    Several other approaches have been attempted on the basis of this model to indicate possible strategies that may lead to disease eradication, but the rather sad conclusion is that they unfortunately do not appear viable in practice. ]]>
Surabhi Pandey and Ezio Venturino Thu, 1 Feb 2018 20:00:00 GMT Three-level global resource allocation model for hiv control: <em>A hierarchical decision system approach</em> Semu Mitiku Kassa Thu, 1 Feb 2018 20:00:00 GMT A frailty model for intervention effectiveness against disease transmission when implemented with unobservable heterogeneity Ping Yan Thu, 1 Feb 2018 20:00:00 GMT Effect of seasonality on the dynamics of an imitation--based vaccination model with public health intervention Bruno Buonomo, Giuseppe Carbone and Alberto d'Onofrio Thu, 1 Feb 2018 20:00:00 GMT Optimal time to intervene: The case of measles child immunization Zuzana Chladná Thu, 1 Feb 2018 20:00:00 GMT