Search for: All records

Abstract Autonomous differential equation compartmental models hold broad utility in epidemiology and public health. However, these models typically cannot account explicitly for myriad factors that affect the trajectory of infectious diseases, with seasonal variations in host behavior and environmental conditions as noteworthy examples. Fortunately, using non-autonomous differential equation compartmental models can mitigate some of these deficiencies, as the inclusion of time-varying parameters can account for temporally varying factors. The inclusion of these temporally varying factors does come at a cost though, as many analysis techniques, such as the use of Poincaré maps and Floquet theory, on non-autonomous differential equation compartmental models are typically only tractable numerically. Here, we illustrate a rare$$n$$ $n$-strain generalized Susceptible-Infectious-Susceptible (SIS) compartmental model, with a general time-varying recovery rate, which features Floquet exponents that are algebraic expressions. We completely characterize the persistence and stability properties of our$$n$$ $n$-strain generalized SIS model for$$n\ge 1$$ $n\ge 1$. We also derive a closed-form solution in terms of elementary functions for the single-strain SIS model, which is capable of incorporating almost any infectious period distribution. Finally, to demonstrate the applicability of our work, we apply it to recent syphilis incidence data from the United States, utilizing Akaike Information Criteria and Forecast Skill Scores to inform on the model’s goodness of fit relative to complexity and the model’s capacity to predict future trends. 

A study in Burkina Faso revealed ivermectin inhibits malaria transmission by killing malaria parasites and mosquitoes. However, it is unknown what effect this drug will have on the malaria transmission intensities of the rest of sub-Saharan Africa (SSA). To address this issue, we created a mathematical model using malaria transmission data from 41 SSA countries to evaluate the antimalarial benefits of a mass drug administration (MDA) of ivermectin. To account for ivermectin's effect on malaria, we incorporate estimates of its ability to inhibit malaria transmission and kill mosquitoes. We consider scenarios where 0, 12.5 %, 25.0 %, and 50.0 % of the population receive ivermectin over five years and estimate malaria incidence averted, disability-adjusted life years saved, and the incremental cost-effectiveness ratio. Our findings show that an MDA of ivermectin to 12.5 %, 25 %, or 50 % of the population annually averts 248.7, 261.4, and 288.7 incidences per thousand people and saves 5.4, 5.7, and 6.3 disability-adjusted life years, respectively. These values indicate that an MDA of ivermectin would be cost-effective in 41, 18, and 6 countries, and very cost-effective in 22, 6, and 3 countries for the 12.5 %, 25 %, and 50 % scenarios. Altogether, our results indicate that ivermectin would prevent a substantial number of malaria incidences and save disability-adjusted life years in the majority of SSA. Therefore, an MDA of ivermectin would greatly aid in ongoing malaria control efforts and should be considered strongly as a complementary intervention to current malaria protocols. 

Differential equation compartmental models are crucial tools for forecasting and analyzing disease trajectories. Among these models, those dealing with only susceptible and infectious individuals are particularly useful as they offer closed-form expressions for solutions, namely the logistic equation. However, the logistic equation has limited ability to describe disease trajectories since its solutions must converge monotonically to either the disease-free or endemic equilibrium, depending on the parameters. Unfortunately, many diseases exhibit periodic cycles, and thus, do not converge to equilibria. To address this limitation, we developed a generalized susceptible-infectious-susceptible compartmental model capable of accurately incorporating the duration of infection distribution and describing both periodic and non-periodic disease trajectories. We characterized how our model’s parameters influence its behavior and applied the model to predict gonorrhea incidence in the US, using Akaike Information Criteria to inform on its merit relative to the traditional SIS model. The significance of our work lies in providing a novel susceptible-infected-susceptible model whose solutions can have closed-form expressions that may be periodic or non-periodic depending on the parameterization. Our work thus provides disease modelers with a straightforward way to investigate the potential periodic behavior of many diseases and thereby may aid ongoing efforts to prevent recurrent outbreaks. 

Sexually transmitted diseases (STDs) are detrimental to the health and economic well-being of society. Consequently, predicting outbreaks and identifying effective disease interventions through epidemiological tools, such as compartmental models, is of the utmost importance. Unfortunately, the ordinary differential equation compartmental models attributed to the work of Kermack and McKendrick require a duration of infection that follows the exponential or Erlang distribution, despite the biological invalidity of such assumptions. As these assumptions negatively impact the quality of predictions, alternative approaches are required that capture how the variability in the duration of infection affects the trajectory of disease and the evaluation of disease interventions. So, we apply a new family of ordinary differential equation compartmental models based on the quantity person-days of infection to predict the trajectory of disease. Importantly, this new family of models features non-exponential and non-Erlang duration of infection distributions without requiring more complex integral and integrodifferential equation compartmental model formulations. As proof of concept, we calibrate our model to recent trends of chlamydia incidence in the U.S. and utilize a novel duration of infection distribution that features periodic hazard rates. We then evaluate how increasing STD screening rates alter predictions of incidence and disability adjusted life-years over a five-year horizon. Our findings illustrate that our family of compartmental models provides a better fit to chlamydia incidence trends than traditional compartmental models, based on Akaike information criterion. They also show new asymptomatic and symptomatic infections of chlamydia peak over drastically different time frames and that increasing the annual STD screening rates from 35% to 40%-70% would annually avert 6.1-40.3 incidence while saving 1.68-11.14 disability adjusted life-years per 1000 people. This suggests increasing the STD screening rate in the U.S. would greatly aid in ongoing public health efforts to curtail the rising trends in preventable STDs.