Mathematical Modeling to Assess the Drivers of the Recent Emergence of Typhoid Fever in Blantyre, Malawi

BACKGROUND: Multiyear epidemics of Salmonella enterica serovar Typhi have been reported from countries across eastern and southern Africa in recent years. In Blantyre, Malawi, a dramatic increase in typhoid fever cases has recently occurred, and may be linked to the emergence of the H58 haplotype. Strains belonging to the H58 haplotype often exhibit multidrug resistance and may have a fitness advantage relative to other Salmonella Typhi strains.

METHODS: To explore hypotheses for the increased number of typhoid fever cases in Blantyre, we fit a mathematical model to culture-confirmed cases of Salmonella enterica infections at Queen Elizabeth Central Hospital, Blantyre. We explored 4 hypotheses: (1) an increase in the basic reproductive number (R0) in response to increasing population density; (2) a decrease in the incidence of cross-immunizing infection with Salmonella Enteritidis; (3) an increase in the duration of infectiousness due to failure to respond to first-line antibiotics; and (4) an increase in the transmission rate following the emergence of the H58 haplotype.

RESULTS: Increasing population density or decreasing cross-immunity could not fully explain the observed pattern of typhoid emergence in Blantyre, whereas models allowing for an increase in the duration of infectiousness and/or the transmission rate of typhoid following the emergence of the H58 haplotype provided a good fit to the data.

CONCLUSIONS: Our results suggest that an increase in the transmissibility of typhoid due to the emergence of drug resistance associated with the H58 haplotype may help to explain recent outbreaks of typhoid in Malawi and similar settings in Africa.

New Method Based on the UNIFAC–VISCO Model for the Estimation of Ionic Liquids Viscosity Using the Experimental Data Recommended by Mathematical Gnostics

The viscosity of ionic liquids (ILs) has been modeled as a function of temperature and at atmospheric pressure using a new method based on the UNIFAC–VISCO method. This model extends the calculations previously reported by our group (see Zhao et al. J. Chem. Eng. Data 2016, 61, 2160–2169) which used 154 experimental viscosity data points of 25 ionic liquids for regression of a set of binary interaction parameters and ion Vogel–Fulcher–Tammann (VFT) parameters. Discrepancies in the experimental data of the same IL affect the quality of the correlation and thus the development of the predictive method. In this work, mathematical gnostics was used to analyze the experimental data from different sources and recommend one set of reliable data for each IL. These recommended data (totally 819 data points) for 70 ILs were correlated using this model to obtain an extended set of binary interaction parameters and ion VFT parameters, with a regression accuracy of 1.4%. In addition, 966 experimental viscosity data points for 11 binary mixtures of ILs were collected from literature to establish this model. All the binary data consist of 128 training data points used for the optimization of binary interaction parameters and 838 test data points used for the comparison of the pure evaluated values. The relative average absolute deviation (RAAD) for training and test is 2.9% and 3.9%, respectively.

Reversibility Iteration Method to Understand Reaction Networks and to Solve Micro-Kinetics in Heterogeneous Catalysis

Solving microkinetics of catalytic systems, which bridges microscopic processes and macroscopic reaction rates, is currently vital for understanding catalysis in silico. However, traditional microkinetic solvers possess several drawbacks that make the process slow and unreliable for complicated catalytic systems. In this paper, a new approach, the so-called reversibility iteration method (RIM), is developed to solve microkinetics for catalytic systems. Using the chemical potential notation we previously proposed to simplify the kinetic framework, the catalytic systems can be analytically illustrated to be logically equivalent to the electric circuit, and the reaction rate and coverage can be calculated by updating the values of reversibilities. Compared to the traditional modified Newton iteration method (NIM), our method is not sensitive to the initial guess of the solution and typically requires fewer iteration steps. Moreover, the method does not require arbitrary-precision arithmetic and has a higher probability of successfully solving the system. These features make it ∼1000 times faster than the modified Newton iteration method for the systems we tested. Moreover, the derived concept and the mathematical framework presented in this work may provide new insight into catalytic reaction networks.