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.

Avoiding Overfitting in Inverse Modeling of Chloride Migration in Concrete

Inverse analysis for reactive transport of chlorides through concrete in the presence of electric field is presented. The model is solved using MATLAB’s built-in solvers “pdepe.m” and “ode15s.m”. The results from the model are compared with experimental measurements from accelerated migration test and a function representing the lack of fit is formed. This function is optimised with respect to varying amount of key parameters defining the model. Levenberg-Marquardt trust-region optimisation approach is employed. The paper presents a method by which the degree of inter-dependency between parameters and sensitivity (significance) of each parameter towards model predictions can be studied on models with or without clearly defined governing equations. Eigen value analysis of the Hessian matrix was employed to investigate and avoid over-parametrisation in inverse analysis. We investigated simultaneous fitting of parameters for diffusivity, chloride binding as defined by Freundlich isotherm (thermodynamic) and binding rate (kinetic parameter). Fitting of more than 2 parameters, simultaneously, demonstrates a high degree of parameter inter-dependency. This finding is significant as mathematical models for representing chloride transport rely on several parameters for each mode of transport (i.e., diffusivity, binding, etc.), which combined may lead to unreliable simultaneous estimation of parameters.