Mathematical modeling and the epidemiological research process

Precision epidemiology at the nexus of mathematics and nanotechnology: Unraveling the dance of viral dynamics

The intersection of mathematical modeling, nanotechnology, and epidemiology marks a paradigm shift in our battle against infectious diseases, aligning with the focus of the journal on the regulation, expression, function, and evolution of genes in diverse biological contexts. This exploration navigates the intricate dance of viral transmission dynamics, highlighting mathematical models as dual tools of insight and precision instruments, a theme relevant to the diverse sections of Gene. In the context of virology, ethical considerations loom large, necessitating robust frameworks to protect individual rights, an aspect essential in infectious disease research. Global collaboration emerges as a critical pillar in our response to emerging infectious diseases, fortified by the predictive prowess of mathematical models enriched by nanotechnology. The synergy of interdisciplinary collaboration, training the next generation to bridge mathematical rigor, biology, and epidemiology, promises accelerated discoveries and robust models that account for real-world complexities, fostering innovation and exploration in the field. In this intricate review, mathematical modeling in viral transmission dynamics and epidemiology serves as a guiding beacon, illuminating the path toward precision interventions, global preparedness, and the collective endeavor to safeguard human health, resonating with the aim of advancing knowledge in gene regulation and expression.

Modeling the effects of drugs of abuse on within-host dynamics of two HIV species

Injection drug use is one of the most significant risk factors associated with contracting human immunodeficiency virus (HIV), and drug users infected with HIV suffer from a higher viral load and rapid disease progression. While replication of HIV may result in many mutant viruses that can escape recognition of the host's immune response, the presence of morphine (a drug of abuse) can decrease the viral mutation rate and cellular immune responses. This study develops a mathematical model to explore the effects of morphine-altered mutation and cellular immune response on the within-host dynamics of two HIV species, a wild-type and a mutant. Our model predicts that the morphine-altered mutation rate and cellular immune response allow the wild-type virus to outcompete the mutant virus, resulting in a higher set point viral load and lower CD4 count. We also compute the basic reproduction numbers and show that the dominant species is determined by morphine concentration, with the mutant dominating below and the wild-type dominating above a threshold. Furthermore, we identified three biologically relevant equilibria, infection-free, mutant-only, and coexistence, which are completely characterized by the fitness cost of mutation, mutant escape rate, and morphine concentration.

Modelling the impact of maternal pneumococcal vaccination on infant pneumococcal disease in low-income settings

Pneumococcal disease is a leading cause of mortality in young children. The largest burden of pneumococcal disease is in the first six months of life before protection from a complete schedule of direct immunisation is possible. Maternal pneumococcal vaccination has been proposed as a strategy for protection in this period of early childhood; however, limited clinical trial data exists. In this study, we developed an age-structured compartmental mathematical model to estimate the impact of maternal pneumococcal vaccination. Our model demonstrates how maternal pneumococcal vaccination could prevent 73% (range 49-88%) of cases in those aged <1 month and 55% (range 36-66%) in those 1-2 months old. This translates to an estimated 17% reduction in deaths due to invasive pneumococcal disease in children under five. Overall, this study demonstrates the potential for maternal pneumococcal vaccination to meaningfully reduce the burden of infant pneumococcal disease, supporting the case for appropriate field-based clinical studies.

Sub-national tailoring of malaria interventions in Mainland Tanzania: simulation of the impact of strata-specific intervention combinations using modelling

Background

To accelerate progress against malaria in high burden countries, a strategic reorientation of resources at the sub-national level is needed. This paper describes how mathematical modelling was used in mainland Tanzania to support the strategic revision that followed the mid-term review of the 2015–2020 national malaria strategic plan (NMSP) and the epidemiological risk stratification at the council level in 2018.

Methods

Intervention mixes, selected by the National Malaria Control Programme, were simulated for each malaria risk strata per council. Intervention mixes included combinations of insecticide-treated bed nets (ITN), indoor residual spraying, larval source management, and intermittent preventive therapies for school children (IPTsc). Effective case management was either based on estimates from the malaria indicator survey in 2016 or set to a hypothetical target of 85%. A previously calibrated mathematical model in OpenMalaria was used to compare intervention impact predictions for prevalence and incidence between 2016 and 2020, or 2022.

Results

For each malaria risk stratum four to ten intervention mixes were explored. In the low-risk and urban strata, the scenario without a ITN mass campaign in 2019, predicted high increase in prevalence by 2020 and 2022, while in the very-low strata the target prevalence of less than 1% was maintained at low pre-intervention transmission intensity and high case management. In the moderate and high strata, IPTsc in addition to existing vector control was predicted to reduce the incidence by an additional 15% and prevalence by 22%. In the high-risk strata, all interventions together reached a maximum reduction of 76%, with around 70% of that reduction attributable to high case management and ITNs. Overall, the simulated revised NMSP was predicted to achieve a slightly lower prevalence in 2020 compared to the 2015–2020 NMSP (5.3% vs 6.3%).

Conclusion

Modelling supported the choice of intervention per malaria risk strata by providing impact comparisons of various alternative intervention mixes to address specific questions relevant to the country. The use of a council-calibrated model, that reproduces local malaria trends, represents a useful tool for compiling available evidence into a single analytical platform, that complement other evidence, to aid national programmes with decision-making processes.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12936-022-04099-5.

Use of mathematical modelling to assess respiratory syncytial virus epidemiology and interventions: a literature review

Respiratory syncytial virus (RSV) is a leading cause of acute lower respiratory tract infection worldwide, resulting in approximately sixty thousand annual hospitalizations of< 5-year-olds in the United States alone and three million annual hospitalizations globally. The development of over 40 vaccines and immunoprophylactic interventions targeting RSV has the potential to significantly reduce the disease burden from RSV infection in the near future. In the context of RSV, a highly contagious pathogen, dynamic transmission models (DTMs) are valuable tools in the evaluation and comparison of the effectiveness of different interventions. This review, the first of its kind for RSV DTMs, provides a valuable foundation for future modelling efforts and highlights important gaps in our understanding of RSV epidemics. Specifically, we have searched the literature using Web of Science, Scopus, Embase, and PubMed to identify all published manuscripts reporting the development of DTMs focused on the population transmission of RSV. We reviewed the resulting studies and summarized the structure, parameterization, and results of the models developed therein. We anticipate that future RSV DTMs, combined with cost-effectiveness evaluations, will play a significant role in shaping decision making in the development and implementation of intervention programs.

Game-Theoretical Model of the Voluntary Use of Insect Repellents to Prevent Zika Fever

Zika fever is an emerging mosquito-borne disease. While it often causes no or only mild symptoms that are similar to dengue fever, Zika virus can spread from a pregnant woman to her baby and cause severe birth defects. There is no specific treatment or vaccine, but the disease can be mitigated by using several control strategies, generally focusing on the reduction in mosquitoes or mosquito bites. In this paper, we model Zika virus transmission and incorporate a game-theoretical approach to study a repeated population game of DEET usage to prevent insect bites. We show that the optimal use effectively leads to disease elimination. This result is robust and not significantly dependent on the cost of the insect repellents.

Risk factors in the illness-death model: Simulation study and the partial differential equation about incidence and prevalence

Recently, we developed a partial differential equation (PDE) that relates the age-specific prevalence of a chronic disease with the age-specific incidence and mortality rates in the illness-death model (IDM). With a view to planning population-wide interventions, the question arises how prevalence can be calculated if the distribution of a risk-factor in the population shifts. To study the impact of such possible interventions, it is important to deal with the resulting changes of risk-factors that affect the rates in the IDM. The aim of this work is to show how the PDE can be used to study such effects on the age-specific prevalence of a chronic disease, to demonstrate its applicability and to compare the results to a discrete event simulation (DES), a frequently used simulation technique. This is done for the first time based on the PDE which only needs data on population-wide epidemiological indices and is related to the von Foerster equation. In a simulation study, we analyse the effect of a hypothetical intervention against type 2 diabetes. We compare the age-specific prevalence obtained from a DES with the results predicted from modifying the rates in the PDE. The DES is based on 10000 subjects and estimates the effect of changes in the distributions of risk-factors. With respect to the PDE, the change of the distribution of risk factors is synthesized to an effective rate that can be used directly in the PDE. Both methods, DES and effective rate method (ERM) are capable of predicting the impact of the hypothetical intervention. The age-specific prevalences resulting from the DES and the ERM are consistent. Although DES is common in simulating effects of hypothetical interventions, the ERM is a suitable alternative. ERM fits well into the analytical theory of the IDM and the related PDE and comes with less computational effort.

Illness-death model: statistical perspective and differential equations

The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

Mathematical Modeling Tools to Study Preharvest Food Safety

This article provides an overview of the emerging field of mathematical modeling in preharvest food safety. We describe the steps involved in developing mathematical models, different types of models, and their multiple applications. The introduction to modeling is followed by several sections that introduce the most common modeling approaches used in preharvest systems. We finish the chapter by outlining potential future directions for the field.

Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease

Background

The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID).

Methods

We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size.

Results

The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia.

Conclusions

Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-015-0953-5) contains supplementary material, which is available to authorized users.

Validation of a population coronary disease predictive system: the CASSANDRA model

BACKGROUND

The use of validated multivariate cardiovascular predictive models in a population setting is of interest for public health policy makers. We aimed to validate the estimations of the CASSANDRA model (coronary heart disease (CHD) incidence and CHD risk distribution), considering the population changes in age, sex and CHD risk factors prevalence in a 10-year period.

METHODS

We compared the projected CHD incidence estimated with CASSANDRA with that observed in the Girona Heart Registry (REGICOR) for 1995-2004 and 2000-2009 in the population of Girona (Spain) aged 35-74 years. We used official age and sex distributions for this population. Baseline cardiovascular risk factors prevalence and the distribution of cardiovascular risk were obtained from three cross-sectional studies performed in 1995, 2000 and 2005. To validate the future distribution of cardiovascular risk, we tested the yearly CHD risk variance over the study period.

RESULTS

No significant differences between the estimated and observed annual CHD incidence per 100 000 men were found in 1995-2004 (CASSANDRA=457.8 and REGICOR=420.3, incidence rate ratio (IRR) (95% CI)=0.92 (0.89 to 0.96)) and in 2000-2009 (441.4 and 409.6, respectively, IRR=0.93 (0.90 to 0.96)). However, overpredictions of 18% and 22%, respectively, were observed in women (198.8 and 160.4, IRR=0.82 (0.77 to 0.86), and 197.1 and 152.8, IRR=0.78 (0.74 to 0.83), respectively). No significant differences were found in the CHD risk variance in the three different cross-sectional studies.

CONCLUSIONS

The CASSANDRA model produces valid estimates, particularly in men, of the future burden of disease and in the distribution of cardiovascular risk in individuals aged 35-74 years.

Modelers' perception of mathematical modeling in epidemiology: a web-based survey

BACKGROUND

Mathematical modeling in epidemiology (MME) is being used increasingly. However, there are many uncertainties in terms of definitions, uses and quality features of MME.

METHODOLOGY/PRINCIPAL FINDINGS

To delineate the current status of these models, a 10-item questionnaire on MME was devised. Proposed via an anonymous internet-based survey, the questionnaire was completed by 189 scientists who had published in the domain of MME. A small minority (18%) of respondents claimed to have in mind a concise definition of MME. Some techniques were identified by the researchers as characterizing MME (e.g. Markov models), while others-at the same level of sophistication in terms of mathematics-were not (e.g. Cox regression). The researchers' opinions were also contrasted about the potential applications of MME, perceived as highly relevant for providing insight into complex mechanisms and less relevant for identifying causal factors. The quality criteria were those of good science and were not related to the size and the nature of the public health problems addressed.

CONCLUSIONS/SIGNIFICANCE

This study shows that perceptions on the nature, uses and quality criteria of MME are contrasted, even among the very community of published authors in this domain. Nevertheless, MME is an emerging discipline in epidemiology and this study underlines that it is associated with specific areas of application and methods. The development of this discipline is likely to deserve a framework providing recommendations and guidance at various steps of the studies, from design to report.