A generalized ODE susceptible-infectious-susceptible compartmental model with potentially periodic behavior.

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.

The effect of screening on the health burden of chlamydia: An evaluation of compartmental models based on person-days of infection.

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.

Inclusive health: modeling COVID-19 in correctional facilities and communities.

BACKGROUND: Mass incarceration, commonly associated with overcrowding and inadequate health resources for incarcerated people, creates a fertile environment for the spread of the coronavirus disease 2019 (COVID-19) in U.S. correctional facilities. The exact role that correctional facilities play in enhancing COVID-19 spread and enabling community re-emergence of COVID-19 is unknown. METHODS: We constructed a novel stochastic model of COVID-19 transmission to estimate the impact of correctional facilities, specifically jails and state prisons, for enhancing disease transmission and enabling disease re-emergence in local communities. Using our model, we evaluated scenarios of testing and quarantining infected incarcerated people at 0.0, 0.5, and 1.0 times the rate that occurs for infected people in the community for population sizes of 5, 10, and 20 thousand people. RESULTS: Our results illustrate testing and quarantining an incarcerated population of 800 would reduce the probability of a major outbreak in the local community. In addition, testing and quarantining an incarcerated population would prevent between 10 to 2640 incidences of COVID-19 per year, and annually save up to 2010 disability-adjusted life years, depending on community size. CONCLUSIONS: Managing COVID-19 in correctional facilities is essential to mitigate risks to community health, and thereby stresses the importance of improving the health standards of incarcerated people.

A generalized differential equation compartmental model of infectious disease transmission.

For decades, mathematical models of disease transmission have provided researchers and public health officials with critical insights into the progression, control, and prevention of disease spread. Of these models, one of the most fundamental is the SIR differential equation model. However, this ubiquitous model has one significant and rarely acknowledged shortcoming: it is unable to account for a disease's true infectious period distribution. As the misspecification of such a biological characteristic is known to significantly affect model behavior, there is a need to develop new modeling approaches that capture such information. Therefore, we illustrate an innovative take on compartmental models, derived from their general formulation as systems of nonlinear Volterra integral equations, to capture a broader range of infectious period distributions, yet maintain the desirable formulation as systems of differential equations. Our work illustrates a compartmental model that captures any Erlang distributed duration of infection with only 3 differential equations, instead of the typical inflated model sizes required by traditional differential equation compartmental models, and a compartmental model that captures any mean, standard deviation, skewness, and kurtosis of an infectious period distribution with 4 differential equations. The significance of our work is that it opens up a new class of easy-to-use compartmental models to predict disease outbreaks that do not require a complete overhaul of existing theory, and thus provides a starting point for multiple research avenues of investigation under the contexts of mathematics, public health, and evolutionary biology.

Advocating an attack against severe malaria: a cost-effectiveness analysis.

BACKGROUND: A recent study found that the gut microbiota, Lactobacillus and Bifidobacterium, have the ability to modulate the severity of malaria. The modulation of the severity of malaria is not however, the typical focal point of most widespread interventions. Thus, an essential element of information required before serious consideration of any intervention that targets reducing severe malaria incidence is a prediction of the health benefits and costs required to be cost-effective. METHODS: Here, we developed a mathematical model of malaria transmission to evaluate an intervention that targets reducing severe malaria incidence. We consider intervention scenarios of a 2-, 7-, and 14-fold reduction in severe malaria incidence, based on the potential reduction in severe malaria incidence caused by gut microbiota, under entomological inoculation rates occurring in 41 countries in sub-Saharan Africa. For each intervention scenario, disability-adjusted life years averted and incremental cost-effectiveness ratios were estimated using country specific data, including the reported proportions of severe malaria incidence in healthcare settings. RESULTS: Our results show that an intervention that targets reducing severe malaria incidence with annual costs between $23.65 to $30.26 USD per person and causes a 14-fold reduction in severe malaria incidence would be cost-effective in 15-19 countries and very cost-effective in 9-14 countries respectively. Furthermore, if model predictions are based on the distribution of gut microbiota through a freeze-dried yogurt that cost $0.20 per serving, a 2- to 14-fold reduction in severe malaria incidence would be cost-effective in 29 countries and very cost-effective in 25 countries. CONCLUSION: Our findings indicate interventions that target severe malaria can be cost-effective, in conjunction with standard interventions, for reducing the health burden and costs attributed to malaria. While our results illustrate a stronger cost-effectiveness for greater reductions, they consistently show that even a limited reduction in severe malaria provides substantial health benefits, and could be economically viable. Therefore, we suggest that interventions that target severe malaria are worthy of consideration, and merit further empirical and clinical investigation.

Fighting the Public Health Burden of AIDS With the Human Pegivirus.

Highly active antiretroviral therapy has revolutionized the battle against human immunodeficiency virus/acquired immune deficiency syndrome (HIV/AIDS). From its current global rollout, HIV/AIDS morbidity and mortality has been greatly reduced, yet there exists substantial interest in the development of new therapies to further mitigate the HIV/AIDS health burden and to inhibit any fallout from the development of antiretroviral drug resistance. One potential intervention is the human pegivirus (HPgV). HPgV is not known to cause disease, and most remarkably it is shown to delay the progression of HIV to AIDS. However, the health benefit of increasing HPgV prevalence in the community of HIV-infected men remains unknown at the public health level. We evaluated the utility of HPgV biovaccination for mitigating the HIV/AIDS health burden using mathematical models. Importantly, our work considers the potential concern that HPgV will, itself, evolve to become disease-causing by permitting mutant disease-causing HPgV strains to potentially arise during treatment. Our findings show that HPgV biovaccination rates of 12.5%-50% annually could prevent 4.2-23.6 AIDS incidences and 3.3-18.8 AIDS deaths, and could save 2.9-18.6 disability-adjusted life years per 1,000 people. Together, these findings indicate that HPgV biovaccination could be an effective therapy for reducing HIV/AIDS morbidity and mortality, and thus warrants further exploration.

Managing Marek's disease in the egg industry.

The industrialization of farming has had an enormous impact. To most, this impact is viewed solely in the context of productivity, but the denser living conditions and shorter rearing periods of industrial livestock farms provide pathogens with an ideal opportunity to spread and evolve. For example, the industrialization of poultry farms drove the Marek's disease virus (MDV) to evolve from a mild paralytic syndrome to a highly contagious, globally prevalent, deadly disease. Fortunately, the economic catastrophe that would occur from MDV evolution is prevented through the widespread use of live imperfect vaccines that limit disease symptoms, but fail to prevent transmission. Unfortunately, the continued rollout of such imperfect vaccines is steering MDV evolution towards even greater virulence, and the ability to evade vaccine protection. Thus, there is a need to investigate alternative economically viable control measures for their ability to inhibit MDV spread and evolution. In what follows we examine the economic viability of standard husbandry practices for their ability to inhibit the spread of both virulent MDV and very virulent MDV throughout an industrialized egg farm. To do this, we parameterize a MDV transmission model and calculate the loss in egg production due to MDV. We find that MDV strain and the cohort duration have the greatest influence on both disease burden and egg production. Additionally, our findings show that for long cohort durations, conventional cages result in the least per capita loss in egg production due to MDV infection, while Aviary systems perform best over shorter cohort durations. Finally, we find that the least per capita loss in egg production for flocks infected with the more virulent MDV strains occurs when cohort durations are sufficiently short. These results highlight the important decisions that managers will face when implementing new hen husbandry practices.

Brief Report: Antimalarial Benefit of HIV Antiretroviral Therapy in Areas of Low to Moderate Malaria Transmission Intensity.

BACKGROUND: We previously used mathematical modeling to predict reduced malaria incidence in children with protease inhibitor (PI)-, compared with nonnucleoside reverse transcriptase inhibitor-, based highly active antiretroviral therapy (HAART), in moderate to high malaria transmission areas. These effects were accounted for, in part, by pharmacokinetic (PK) interactions between PIs and artemether-lumefantrine (AL). OBJECTIVE: Because of potentially reduced malaria transmission reservoirs in HIV-infected children due to PI/AL PK interactions impacting non-HIV-infected children, we estimate the antimalarial benefit of PI-based HAART in all children, and in HIV-infected children only residing in low to moderate malaria transmission areas. DESIGN: A dynamic model of malaria transmission was developed to evaluate the PK interaction of PI-based HAART with the antimalarial, AL for preventing malaria. METHODS: To evaluate the benefit of HIV PI-based HAART on malaria incidence, a malaria transmission model with varying degrees of HIV newborn prevalence was developed using recent pediatric clinical trial data in Lilongwe, Malawi. RESULTS: Comparing situations of low to high HIV newborn prevalence, and low to moderate malaria transmission intensities, our model predicts the combination of PI-based HAART with AL-treated malaria prevents 0.04-24.8 and 0.05-34.5 annual incidences of malaria overall per 1000 children, and saves 0.003-1.66 and 0.003-2.30 disability-adjusted life years per 1000 children, respectively. When incorporating seasonality, 0.01-7.3 and 0.01-5.9 annual incidences of malaria overall per 1000 children, and 0.0-0.5 and 0.001-0.41 disability-adjusted life years per 100 children, are prevented, respectively. CONCLUSIONS: In low to moderate malaria transmission intensity areas, PI-based HAART may reduce malaria events in children when AL is used.

Modelling the impact of antimalarial quality on the transmission of sulfadoxine-pyrimethamine resistance in Plasmodium falciparum.

BACKGROUND: The use of poor quality antimalarial medicines, including the use of non-recommended medicines for treatment such as sulfadoxine-pyrimethamine (SP) monotherapy, undermines malaria control and elimination efforts. Furthermore, the use of subtherapeutic doses of the active ingredient(s) can theoretically promote the emergence and transmission of drug resistant parasites. METHODS: We developed a deterministic compartmental model to quantify the impact of antimalarial medicine quality on the transmission of SP resistance, and validated it using sensitivity analysis and a comparison with data from Kenya collected in 2006. We modelled human and mosquito population dynamics, incorporating two Plasmodium falciparum subtypes (SP-sensitive and SP-resistant) and both poor quality and good quality (artemether-lumefantrine) antimalarial use. FINDINGS: The model predicted that an increase in human malaria cases, and among these, an increase in the proportion of SP-resistant infections, resulted from an increase in poor quality SP antimalarial use, whether it was full- or half-dose SP monotherapy. INTERPRETATION: Our findings suggest that an increase in poor quality antimalarial use predicts an increase in the transmission of resistance. This highlights the need for stricter control and regulation on the availability and use of poor quality antimalarial medicines, in order to offer safe and effective treatments, and work towards the eradication of malaria.

Time-varying and state-dependent recovery rates in epidemiological models.

Differential equation models of infectious disease have undergone many theoretical extensions that are invaluable for the evaluation of disease spread. For instance, while one traditionally uses a bilinear term to describe the incidence rate of infection, physically more realistic generalizations exist to account for effects such as the saturation of infection. However, such theoretical extensions of recovery rates in differential equation models have only started to be developed. This is despite the fact that a constant rate often does not provide a good description of the dynamics of recovery and that the recovery rate is arguably as important as the incidence rate in governing the dynamics of a system. We provide a first-principles derivation of state-dependent and time-varying recovery rates in differential equation models of infectious disease. Through this derivation, we demonstrate how to obtain time-varying and state-dependent recovery rates based on the family of Pearson distributions and a power-law distribution, respectively. For recovery rates based on the family of Pearson distributions, we show that uncertainty in skewness, in comparison to other statistical moments, is at least two times more impactful on the sensitivity of predicting an epidemic's peak. In addition, using recovery rates based on a power-law distribution, we provide a procedure to obtain state-dependent recovery rates. For such state-dependent rates, we derive a natural connection between recovery rate parameters with the mean and standard deviation of a power-law distribution, illustrating the impact that standard deviation has on the shape of an epidemic wave.

Disease elimination and re-emergence in differential-equation models.

Traditional differential equation models of disease transmission are often used to predict disease trajectories and evaluate the effectiveness of alternative intervention strategies. However, such models cannot account explicitly for probabilistic events, such as those that dominate dynamics when disease prevalence is low during the elimination and re-emergence phases of an outbreak. To account for the dynamics at low prevalence, i.e. the elimination and risk of disease re-emergence, without the added analytical and computational complexity of a stochastic model, we develop a novel application of control theory. We apply our approach to analyze historical data of measles elimination and re-emergence in Iceland from 1923 to 1938, predicting the temporal trajectory of local measles elimination and re-emerge as a result of disease migration from Copenhagen, Denmark.

The epidemiological impact of HIV antiretroviral therapy on malaria in children.

OBJECTIVE: The objective of this study is to determine the epidemiological effectiveness of a first-line antiretroviral regimen with HIV protease inhibitor for preventing recurrent malaria in children under the range of HIV prevalence levels and malaria transmission intensities encountered in sub-Saharan Africa. DESIGN: A dynamic model of malaria transmission was developed using clinical data on the protease inhibitor extended posttreatment prophylactic effect of the antimalarial treatment, artemether-lumefantrine, in addition to parameter estimates from the literature. METHODS: To evaluate the benefits of HIV protease inhibitors on the health burden of recurrent malaria among children, we constructed a dynamic model of malaria transmission to both HIV-positive and HIV-negative children, parameterized by data from a recent clinical trial. The model was then evaluated under varying malaria transmission and HIV prevalence settings to determine the health benefits of HIV protease inhibitors in the context of artemether-lumefantrine treatment of malaria in children. RESULTS: Comparing scenarios of low, intermediate and high newborn HIV prevalence, in a range of malaria transmission settings, our dynamic model predicts that artemether-lumefantrine with HIV protease inhibitor based regimens prevents 0.03-0.10, 5.2-13.0 and 25.5-65.8 annual incidences of malaria per 1000 children, respectively. In addition, HIV protease inhibitors save 0.002-0.006, 0.22-0.8, 1.04-4.3 disability-adjusted life-years per 1000 children annually. Considering only HIV-infected children, HIV protease inhibitors avert between 278 and 1043 annual incidences of malaria per 1000 children. CONCLUSION: The use of HIV protease inhibitor based regimens as first-line antiretroviral therapy for HIV is an effective measure for reducing recurrent malaria among HIV-infected children in areas where HIV and malaria are coendemic, and artemether-lumefantrine is a first-line antimalarial.

Impact of Schistosoma mansoni on malaria transmission in Sub-Saharan Africa.

BACKGROUND: Sub-Saharan Africa harbors the majority of the global burden of malaria and schistosomiasis infections. The co-endemicity of these two tropical diseases has prompted investigation into the mechanisms of coinfection, particularly the competing immunological responses associated with each disease. Epidemiological studies have shown that infection with Schistosoma mansoni is associated with a greater malaria incidence among school-age children. METHODOLOGY: We developed a co-epidemic model of malaria and S. mansoni transmission dynamics which takes into account key epidemiological interaction between the two diseases in terms of elevated malaria incidence among individuals with S. mansoni high egg output. The model was parameterized for S. mansoni high-risk endemic communities, using epidemiological and clinical data of the interaction between S. mansoni and malaria among children in sub-Saharan Africa. We evaluated the potential impact of the S. mansoni-malaria interaction and mass treatment of schistosomiasis on malaria prevalence in co-endemic communities. PRINCIPAL FINDINGS: Our results suggest that in the absence of mass drug administration of praziquantel, the interaction between S. mansoni and malaria may reduce the effectiveness of malaria treatment for curtailing malaria transmission, in S. mansoni high-risk endemic communities. However, when malaria treatment is used in combination with praziquantel, mass praziquantel administration may increase the effectiveness of malaria control intervention strategy for reducing malaria prevalence in malaria- S. mansoni co-endemic communities. CONCLUSIONS/SIGNIFICANCE: Schistosomiasis treatment and control programmes in regions where S. mansoni and malaria are highly prevalent may have indirect benefits on reducing malaria transmission as a result of disease interactions. In particular, mass praziquantel administration may not only have the direct benefit of reducing schistosomiasis infection, it may also reduce malaria transmission and disease burden.