Search

We extend the adaptive moving mesh (AMM) central-upwind schemes recently proposed in Kurganov et al. [Commun. Appl. Math. Comput. 3 (2021) 445–479] in the context of one- (1-D) and two-dimensional (2-D) Euler equations of gas dynamics and granular hydrodynamics, to the 1-D and 2-D Saint-Venant system of shallow water equations. When the bottom topography is nonflat, these equations form hyperbolic systems of balance laws, for which a good numerical method should be capable of preserving a delicate balance between the flux and source terms as well as preserving the nonnegativity of water depth even in the presence of dry or almost dry regions. Therefore, in order to extend the AMM central-upwind schemes to the Saint-Venant systems, we develop special positivity preserving reconstruction and evolution steps of the AMM algorithms as well as special corrections of the solution projection step in (almost) dry areas. At the same time, we enforce the moving mesh to be structured even in the case of complicated 2-D computational domains. We test the designed method on a number of 1-D and 2-D examples that demonstrate robustness and high resolution of the proposed numerical approach.

Background We assessed the cost-effectiveness of the Check It program, a novel community-based chlamydia screening and expedited partner treatment program for young Black men conducted in New Orleans since 2017. Methods We implemented a probabilistic cost-effectiveness model using a synthetic cohort of 16 181 men and 13 419 women intended to simulate the size of the Black, sexually active population in New Orleans ages 15–24 years. Results The Check It program cost $196 838 (95% confidence interval [CI]: $117 320–$287 555) to implement, saved 10.2 quality-adjusted life-years (QALYs; 95% CI: 7.7–12.7 QALYs), and saved $140 950 (95% CI: −$197 018 to −$105 620) in medical costs per year. The program cost $5468 (95% CI: cost saving, $16 717) per QALY gained. All iterations of the probabilistic model returned cost-effectiveness ratios less than $50 000 per QALY gained. Conclusions The Check It program (a bundled seek, test, and treat chlamydia prevention program for young Black men) is cost-effective under base case assumptions. Communities where Chlamydia trachomatis rates have not declined could consider implementing a similar program.

We describe an approach to generate a heterosexual network with a prescribed joint-degree distribution embedded in a prescribed large-scale social contact network. The structure of a sexual network plays an important role in how all sexually transmitted infections (STIs) spread. Generating an ensemble of networks that mimics the real-world is crucial to evaluating robust mitigation strategies for controlling STIs. Most of the current algorithms to generate sexual networks only use sexual activity data, such as the number of partners per month, to generate the sexual network. Real-world sexual networks also depend on biased mixing based on age, location, and social and work activities. We describe an approach to use a broad range of social activity data to generate possible heterosexual networks. We start with a large-scale simulation of thousands of people in a city as they go through their daily activities, including work, school, shopping, and activities at home. We extract a social network from these activities where the nodes are the people, and the edges indicate a social interaction, such as working in the same location. This social network captures the correlations between people of different ages, living in different locations, their economic status, and other demographic factors. We use the social contact network to define a bipartite heterosexual network that is embedded within an extended social network. The resulting sexual network captures the biased mixing inherent in the social network, and models based on this pairing of networks can be used to investigate novel intervention strategies based on the social contacts among infected people. We illustrate the approach in a model for the spread of chlamydia in the heterosexual network representing the young sexually active community in New Orleans.

We develop and analyze a stage-progression compartmental model to study the emerging invasive nontyphoidal Salmonella (iNTS) epidemic in sub-Saharan Africa. iNTS bloodstream infections are often fatal, and the diverse and non-specific clinical features of iNTS make it difficult to diagnose. We focus our study on identifying approaches that can reduce the incidence of new infections. In sub-Saharan Africa, transmission and mortality are correlated with the ongoing HIV epidemic and severe malnutrition. We use our model to quantify the impact that increasing antiretroviral therapy (ART) for HIV infected adults and reducing malnutrition in children would have on mortality from iNTS in the population. We consider immunocompromised subpopulations in the region with major risk factors for mortality, such as malaria and malnutrition among children and HIV infection and ART coverage in both children and adults. We parameterize the progression rates between infection stages using the branching probabilities and estimated time spent at each stage. We interpret the basic reproduction number R0 as the total contribution from an infinite infection loop produced by the asymptomatic carriers in the infection chain. The results indicate that the asymptomatic HIV+ adults without ART serve as the driving force of infection for the iNTS epidemic. We conclude that the worst disease outcome is among the pediatric population, which has the highest infection rates and death counts. Our sensitivity analysis indicates that the most effective strategies to reduce iNTS mortality in the studied population are to improve the ART coverage among high-risk HIV+ adults and reduce malnutrition among children.

We introduce adaptive moving mesh central-upwind schemes for one- and two-dimensional hyperbolic systems of conservation and balance laws. The proposed methods consist of three steps. First, the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh. When the evolution step is complete, the grid points are redistributed according to the moving mesh differential equation. Finally, the evolved solution is projected onto the new mesh in a conservative manner. The resulting adaptive moving mesh methods are applied to the one- and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems. Our numerical results demonstrate that in both cases, the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.

Aedes-borne viral diseases such as dengue fever are surging in incidence in recent years. To investigate viral transmission risks, the availability of local transmission parameters is essential. One of the most important factors directly determining infection risk is human–mosquito contact. Yet the contact rate is not often characterized, compared with other risk metrics such as vector density, because of the limited research tool options. In this study, human–mosquito contact was assessed in two study sites in the Southern United States using self-administered standardized survey instruments. The fraction of mosquito bites attributed to important vector species was estimated by human landing sampling. The survey participants reported a significantly higher outdoor mosquito bite exposure than indoor. The reported bite number was positively correlated with outdoor time during at-risk periods. There was also a significant effect of the study site on outdoor bite exposure, possibly due to the differing vector density. Thus, the levels of human–mosquito contact in this study were influenced both by the mosquito density and human behaviors. A dengue virus transmission model demonstrated that the observed difference in the contact rates results in differential virus transmission risks. Our findings highlight the practicality of using surveys to investigate human–mosquito contact in a setting where bite exposure levels differ substantially, and serve as a basis for further evaluations. This study underscores a new avenue that can be used in combination with other field methods to understand how changes in human behavior may influence mosquito bite exposure which drives mosquito-borne virus transmission.

Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as dengue fever, Zika, and chikungunya. Field trials and modeling studies have shown that the fraction of infection among the mosquitoes must exceed a threshold level for the infection to persist. To capture this threshold, it is critical to consider the spatial heterogeneity in the distributions of the infected and uninfected mosquitoes, which is created by the local release of the infected mosquitoes. We develop and analyze partial differential equation (PDE) models to study the invasion dynamics of Wolbachia infection among mosquitoes in the field. Our reaction-diffusion-type models account for both the complex vertical transmission and the spatial mosquito dispersion. We characterize the threshold for a successful invasion, which is a bubble-shaped profile, called the "critical bubble". The critical bubble is optimal in its release size compared to other spatial profiles in a one-dimensional landscape. The fraction of infection near the release center is higher than the threshold level for the corresponding homogeneously mixing ODE models. We show that the proposed spatial models give rise to the traveling waves of Wolbachia infection when above the threshold. We quantify how the threshold condition and traveling-wave velocity depend on the diffusion coefficients and other model parameters. Numerical studies for different scenarios are presented to inform the design of release strategies., Comment: Submitted

Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development. Thus the value of understanding the impact of immunological parameters on epidemiological quantities. Here we consider an age-since-infection structured vector-host model, in which epidemiological parameters are formulated as functions of within-host virus and antibody densities, governed by an ODE system. We then use SA for these immuno-epidemiological models to investigate the impact of immunological parameters on population-level disease dynamics such as basic reproduction number, final size of the epidemic or the infectiousness at different phases of an outbreak. As a case study, we consider Rift Valley Fever Disease utilizing parameter estimations from prior studies. SA indicates that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\%$$\end{document}1% increase in within-host pathogen growth rate can lead up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$8\%$$\end{document}8% increase in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal R_0,$$\end{document}R0, up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1 \%$$\end{document}1% increase in steady-state infected host abundance, and up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\%$$\end{document}4% increase in infectiousness of hosts when the reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal R_0$$\end{document}R0 is larger than one. These significant increases in population-scale disease quantities suggest that control strategies that reduce the within-host pathogen growth can be important in reducing disease prevalence.

We create and analyze a hierarchy of reduced order models for the spread of a Wolbachia bacteria infection in mosquitoes. Mosquitoes that are infected with some strains of the Wolbachia bacteria ar...

Chlamydia trachomatis (Ct) is the most reported sexually transmitted infection in the United States, with a major cause of infertility, pelvic inflammatory disease, and ectopic pregnancy among women. Despite decades of screening women for Ct, rates increase among young African Americans (AA). We create and analyze a heterosexual agent-based network model to help understand the spread of Ct. We calibrate the model parameters to agree with survey data showing Ct prevalence of 12% of the women and 10% of the men in the 15-25 year-old AA in New Orleans, Louisiana. Our model accounts for both long-term and casual partnerships. The network captures the assortative mixing of individuals by preserving the joint-degree distributions observed in the data. We compare the effectiveness of intervention strategies based on randomly screening men, notifying partners of infected people, which includes partner treatment, partner screening, and rescreening for infection. We compare the difference between treating partners of an infected person both with and without testing them. We observe that although increased Ct screening, rescreening, and treating most of the partners of infected people will reduce the prevalence, these mitigations alone are not sufficient to control the epidemic. The current practice is to treat the partners of an infected individual without first testing them for infection. The model predicts that if a sufficient number of the partners of all infected people are tested and treated, then there is a threshold condition where the epidemic can be mitigated. This threshold results from the expanded treatment network created by treating an individual's infected partners' partners. Although these conclusions can help design future Ct mitigation studies, we caution the reader that these conclusions are for the mathematical model, not the real world, and are contingent on the validity of the model assumptions.

Aedes-borne viral diseases, including dengue fever, chikungunya, and Zika, have been surging in incidence and spreading to new areas where their mosquito vectors thrive. To estimate viral transmission risks, availability of accurate local transmission parameters is essential. One of the most important parameters to determine infection risk is the human-mosquito contact rate. However, this rate has rarely been characterized due to the lack of a feasible research method. In this study, human-mosquito contact rates were evaluated in two study sites within the Greater New Orleans Region by asking a group of survey participants to estimate mosquito bites they experienced in the past 24 hours. The fraction of the mosquito bites attributed to Ae. aegypti or Ae. albopictus was estimated by human landing sampling. The results showed a significantly higher outdoor mosquito bite exposure than indoor exposure. The number of reported mosquito bites was positively correlated with the time that study participants spent outside during at-risk periods. There was also a significant effect of the study site on outdoor bite exposure, possibly because of the difference in the numbers of host-seeking mosquitoes. We use a mathematical dengue virus transmission model to estimate the transmission risks in the study areas based on local conditions. This compartmental model demonstrated how the observed difference in the human-Aedes contact rates in the two study sites would result in differential dengue transmission risks. This study highlights the practicality of using a survey to estimate human-mosquito contact rates and serves as a basis for future evaluations. Combined with the use of mathematical modeling, this innovative method may lead to more effective mosquito-borne pathogen prevention and control.Author summaryEven though the human-mosquito contact rate is among the most important indicators of mosquito-borne viral transmission risk, it is rarely characterized in the field. Human Landing Capture is a gold standard method to quantify this rate, but it ignores variables such as human behaviors and lifestyles. In this study, we tested the feasibility of using surveys to quantify mosquito bite exposure in the Southern United States. The survey results, combined with mosquito species proportion data, were used to estimate the contact rate. These rates are key parameters used in mathematical models to determine transmission risks. We found that bite exposure occurred more often outside homes and people who spent more time outdoors in the evening and night had a higher exposure. Our model analysis shows that the human-mosquito contact rate is one of the most important parameters determining outbreak potential. Disease control programs should focus their efforts on reducing this rate in addition to the mosquito density. Future studies should test if the entomological contact rates described by surveys correlate with disease incidences or other entomological indices. This study highlights the importance of characterizing how vector-human contact rates may respond to changing human behaviors and environments.

In this paper, we propose a fast explicit operator splitting method to solve the modified Buckley---Leverett equations which include a third-order mixed derivatives term resulting from the dynamic effects in the pressure difference between the two phases. The method splits the original equation into two equations, one with a nonlinear convective term and the other one with high-order linear terms so that appropriate numerical methods can be applied to each of the split equations: the high-order linear equation is numerically solved using a pseudo-spectral method, while the nonlinear convective equation is integrated using the Godunov-type central-upwind scheme. The spatial order of the central-upwind scheme depends on the order of the piecewise polynomial reconstruction: we test both the second-order minmod-based reconstruction and fifth-order WENO5 one to demonstrate that using higher-order spatial reconstruction leads to more accurate approximation of solutions. A variety of numerical examples in both one and two space dimensions show that the solutions may have many different saturation profiles depending on the initial conditions, diffusion parameter, and the third-order mixed derivatives parameter. The results are consistent with the study of traveling wave solutions and their bifurcation diagrams.