A Mathematical Model Analysis for the Transmission Dynamics of Leptospirosis Disease in Human and Rodent Populations

Optimal control and cost-effectiveness analysis for leptospirosis epidemic

This paper aims to apply an optimal control theory for the autonomous model of the leptospirosis epidemic to examine the effect of four time-dependent control measures on the model dynamics with cost-effectiveness. Pontryagin's Maximum Principle was used to derive the optimality system associated with the optimal control problem. Numerical simulations of the optimality system were performed for different control strategies and the results were presented graphically with and without controls. The optimality system was simulated using the Forward-Backward Sweep method in the Matlab programme. The numerical results revealed that the combination of all optimal control measures is the most effective strategy for minimizing the spread and impact of disease in the community. Furthermore, a cost-effectiveness analysis was performed to determine the most cost-effective strategy using the incremental cost-effectiveness ratio approach and we observed that the rodenticide control-only strategy is most effective to combat the spread of disease when available resources are limited.

Wastewater surveillance beyond COVID-19: a ranking system for communicable disease testing in the tri-county Detroit area, Michigan, USA

Introduction

Throughout the coronavirus disease 2019 (COVID-19) pandemic, wastewater surveillance has been utilized to monitor the disease in the United States through routine national, statewide, and regional monitoring projects. A significant canon of evidence was produced showing that wastewater surveillance is a credible and effective tool for disease monitoring. Hence, the application of wastewater surveillance can extend beyond monitoring SARS-CoV-2 to encompass a diverse range of emerging diseases. This article proposed a ranking system for prioritizing reportable communicable diseases (CDs) in the Tri-County Detroit Area (TCDA), Michigan, for future wastewater surveillance applications at the Great Lakes Water Authority's Water Reclamation Plant (GLWA's WRP).

Methods

The comprehensive CD wastewater surveillance ranking system (CDWSRank) was developed based on 6 binary and 6 quantitative parameters. The final ranking scores of CDs were computed by summing the multiplication products of weighting factors for each parameter, and then were sorted based on decreasing priority. Disease incidence data from 2014 to 2021 were collected for the TCDA. Disease incidence trends in the TCDA were endowed with higher weights, prioritizing the TCDA over the state of Michigan.

Results

Disparities in incidences of CDs were identified between the TCDA and state of Michigan, indicating epidemiological differences. Among 96 ranked CDs, some top ranked CDs did not present relatively high incidences but were prioritized, suggesting that such CDs require significant attention by wastewater surveillance practitioners, despite their relatively low incidences in the geographic area of interest. Appropriate wastewater sample concentration methods are summarized for the application of wastewater surveillance as per viral, bacterial, parasitic, and fungal pathogens.

Discussion

The CDWSRank system is one of the first of its kind to provide an empirical approach to prioritize CDs for wastewater surveillance, specifically in geographies served by centralized wastewater collection in the area of interest. The CDWSRank system provides a methodological tool and critical information that can help public health officials and policymakers allocate resources. It can be used to prioritize disease surveillance efforts and ensure that public health interventions are targeted at the most potentially urgent threats. The CDWSRank system can be easily adopted to geographical locations beyond the TCDA.

A mathematical model analysis of the human melioidosis transmission dynamics with an asymptomatic case

In this paper, we develop and examine a mathematical model of human melioidosis transmission with asymptomatic cases to describe the dynamics of the epidemic. The basic reproduction number ( R 0 ) of the model is obtained. Disease-free equilibrium of the model is proven to be globally asymptotically stable whenR 0 is less than the unity, while the endemic equilibrium of the model is shown to be locally asymptotically stable ifR 0 is greater than unity. Sensitivity analysis is performed to illustrate the effect of the model parameters influencing on the disease dynamics. Furthermore, numerical experiments of the model are conducted to validate the theoretical findings.