Optimal control for an age-structured model for the transmission of hepatitis B.

One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention.

Multiscale modelling of hepatitis B virus at cell level of organization.

Multiscale modelling is a promising quantitative approach for studying infectious disease dynamics. This approach garners attention from both individuals who model diseases and those who plan for public health because it has great potential to contribute in expanding the understanding necessary for managing, reducing, and potentially exterminating infectious diseases. In this article, we developed a nested multiscale model of hepatitis B virus (HBV) that integrates the within-cell scale and the between-cell scale at cell level of organization of this disease system. The between-cell scale is linked to the within-cell scale by a once off inflow of initial viral infective inoculum dose from the between-cell scale to the within-cell scale through the process of infection; the within-cell scale is linked to the between-cell scale through the outflow of the virus from the within-cell scale to the between-cell scale through the process of viral shedding or excretion. The resulting multiple scales model is bidirectionally coupled in such a way that the within-cell scale and between-cell scale sub-models mutually affect each other, creating a reciprocal relationship. The computed reproductive number from the multiscale model confirms that the within-host scale and the between-host scale influence each other in a reciprocal manner. Numerical simulations are presented that also confirm the theoretical results and support the initial assumption that the within-cell scale and the between-cell scale influence each other in a reciprocal manner. This multiple scales modeling approach serves as a valuable tool for assessing the impact and success of health strategies aimed at controlling hepatitis B virus disease system.

High level of intrinsic phenotypic antimicrobial resistance in enterobacteria from terrestrial wildlife in Gabonese national parks.

Data on the prevalence of antibiotic resistance in Enterobacteriaceae in African wildlife are still relatively limited. The aim of this study was to estimate the prevalence of phenotypic intrinsic and acquired antimicrobial resistance of enterobacteria from several species of terrestrial wild mammals in national parks of Gabon. Colony culture and isolation were done using MacConkey agar. Isolates were identified using the VITEK 2 and MALDI-TOF methods. Antibiotic susceptibility was analysed and interpreted according to the European Committee on Antimicrobial Susceptibility Testing guidelines. The preliminary test for ESBL-producing Enterobacteriaceae was performed by replicating enterobacterial colonies on MacConkey agar supplemented with 2 mg/L cefotaxime (MCA+CTX). Extended-spectrum beta-lactamase (ESBL) production was confirmed with the double-disc synergy test (DDST). The inhibition zone diameters were read with SirScan. Among the 130 bacterial colonies isolated from 125 fecal samples, 90 enterobacterial isolates were identified. Escherichia coli (61%) was the most prevalent, followed by Enterobacter cloacae (8%), Proteus mirabilis (8%), Klebsiella variicola (7%), Klebsiella aerogenes (7%), Klebsiella oxytoca (4%), Citrobacter freundii (3%), Klebsiella pneumoniae (1%) and Serratia marcescens (1%). Acquired resistance was carried by E. coli (11% of all E. coli isolates) and E. cloacae (3% of all E. cloacae) isolates, while intrinsic resistance was detected in all the other resistant isolates (n = 31); K. variicola, K. oxytoca, K. pneumoniae, E. cloacae, K. aerogenes, S. marcescens and P. mirabilis). Our data show that most strains isolated in protected areas in Gabon are wild type isolates and carry intrinsic resistance rather than acquired resistance.

Modelling and control of a banana soilborne pest in a multi-seasonal framework.

We study the infestation dynamics of banana or plantain plants by Radopholus similis, a plant-parasitic nematode that causes severe damages. Two control strategies are implemented in our model: pesticides, which are widely used, and fallows, which are more environmentally friendly. To represent the host-parasite dynamics, two semi-discrete models are proposed. During each cropping season, free nematodes enter the plant roots, on which they feed and reproduce. At the end of the cropping season, fruits are harvested. In the first model, the parent plant is cut down to be replaced by one of its suckers and pesticides are applied. In the second model, the parent plant is uprooted and a fallow period is introduced, inducing the decay of the free pest populations; at the beginning of the next cropping season, a pest-free vitroplant is planted. For both models, the effective reproduction number of pests is computed, assuming that the infestation dynamics are fast compared to the other processes, which leads to the model order reduction. Conditions on the pesticide load or the fallow duration are then derived to ensure the stability of the periodic pest free solution. Finally, numerical simulations illustrate these theoretical results.

Global stability analysis for SEIS models with n latent classes.

We compute the basic reproduction ratio of a SEIS model with n classes of latent individuals and bilinear incidence. The system exhibits the traditional behaviour. We prove that if R(0) < or = 1, then the disease-free equilibrium is globally asymptotically stable on the nonnegative orthant and if R (0) > 1, an endemic equilibrium exists and is globally asymptotically stable on the positive orthant.