Ahmad, Nura M.R.

López Codina, Daniel

Montañola Sales, Cristina

R. Ahmad, Nura M.

UPCommons

Effect of population structure, parameter estimation of complex model, and LTBI on TB dynamics

UPCommons. Portal del coneixement obert de la UPC

Effect of population structure, parameter estimationof complex model, and LTBI on TB dynamicsNura M. R. Ahmad∗, Cristina Montan˜ola-Sales†, Daniel Lo´pez Codinac´∗∗Department of Physics(BIOCOM), UPC, BarcelonaTech†Barcelona Supercomputing Center (BSC), Jordi Girona 29, 08034 BarcelonaE-mail: {nura.mohammad.rabiu.ahmad, daniel.lopez-codina, cristina.montanola}@upc.eduKeywords—TB, complex model, parameter estimation, LTBI,age of infection, structure of population, infectious disease.I. EXTENDED ABSTRACTThe intricate nature of Tuberculosis (TB) infection requiresfurther research to better understand the relationship betweenthe disease mechanisms and the population structure. Theinfluence of the population structure and the role of the infectedpopulation on the TB incidence is still not clear. In this study,mathematical modelling techniques are used to elucidate thosequestions and contribute to understand TB complexity. Thework examines the complexity of TB dynamics by using SEImodels of different levels of complexity to study the effectof both structure of population and the role of the infectedpopulation in TB dynamics. It presents a step by step procedureof how to develop and estimate parameters of complex modelfor TB transmission. We performed different experiment onmore than 20 different countries in order to elucidate if theincrease in complexity of the models increases the modelaccuracy and provides more information about the disease. Ourresults indicate that parameter estimation could be made easyby the gradual development of simple models. In addition weshowed the importance of more complex model over simplemodel and our result indicate that, unlike simple models,complex model could explain characteristic of the disease suchas diagnosis delay time and reinfection. We illustrate how themodel without population as a limiting factor dramatic changein behaviour when implemented in high burden incidence. Wealso demonstrate how the change in age of infection in thelatent TB could dramatically alter the dynamics of the disease.A. IntroductionTuberculosis (TB) is still a major global health concern andone of the leading causes of death. As reported by WHO, therewere an estimated 10.4 million new incident TB cases and 1.7million deaths worldwide in 2015[1]. Even though most TBcases occur in resource-limited countries, it is still a threatto higher-resource countries. This is due to the nature of thedisease’s strong interaction with HIV dynamics and also therecently world-wide emergence of drug-resistant TB [2], [3].The main manifestation and the only infectious form of TBis the pulmonary form, hence worthy of study. Pulmonary TBis an infectious disease caused by Mycobacterium tuberculosis(Mtb) and it is transmitted via air borne droplets of the saliva ofthe sick host. When a sick host sneezes, coughs or talks it caninfect susceptible individuals sharing the same environmentwho inhale the saliva droplets containing the bacterium. Theinhalation of the bacilli will usually lead to the initiation of animmune response that can have one of the 3 different clinicaloutcomes: (1) Complete clearance of the pathogen (2) LatentTB infection (LTBI) or (3) Progression to primary active dis-ease [4], [5]. The objectives of this study are: (i) To understandhow the structure of the population that can shape the dynamicsof the disease.(i) To show the importance of both complexand simple models depending on each given situation, andto elucidate how parameter estimation can be easily achievedwhen developing gradually more complex models.(iii) To showthe role and importance of the latent infected population andthe age of infection in understanding the dynamics of TB.The epidemiological evolution of 20 different countries will beanalyzed to exemplify the importance of each type of modelto achieve the aims set above.B. MethodologyTB dynamics presents several characteristics that greatlycontribute to its complexity. Compartmental models facilitateobtaining a good understanding of these complexity. Fig. 1proposed several compartmental models that were used todescribed the dynamics of TB with different complexity level.In each of the model, starting with the most simple form SEI,population were divided into different compartment, namelySusceptible S, latent infected (exposed) E, Sick (infectious) I,and Reinfection R. We formulated five different models (SEI,SEI2, SE8I, SE8I2, SE8IR), each model was formulated withtwo different force of infection Λ =αISNand Λ∗ = αI toallow the evaluation of effect of population on the dynamics ofthe disease. Model equation for each model were formulated,and the spectral radius was analyzes.C. ResultsTB epidemiological data from countries all around theworld was analyzed and 20 (10 LBC and 10 HBC) differentcountries were selected to test and validate the models.Comparison of models performance between low and highincidence burden setting to illustrate the effect of populationon Tb dynamics: To address the long over due question ofhow the population can affect the dynamics of TB, we adhereto our strategy by fitting both set of models with populationas limiting factor and without to both LBC and HBC. Fig. 2illustrate the difference between the two sets of models whenimplemented in low burden and high burden countries.5th BSC Severo Ochoa Doctoral Symposium38Fig. 1. Overview of several proposed compartment models with differentlevel of complexity. SEI is the classical model of three compartments usedto understand the epidemiological dynamics of TB in a given population.SEI2 applies to a general context of TB dynamics and has four compartments(Susceptible S; Exposed E; sick and infectious I1; and sick but not infectiousI2). SE8I refers to a context where the time scale and age of infectionin the latently infected population is considered due to its importance inunderstanding TB dynamics. In SE8I2 two main important features werealso added, the diagnosis time delay and the probability of relapse. Thesick population are dived into two sub-population, I1 sick and infectious(thus, spreading the disease) and I2 sick but under treatment. Finally, incontexts of high incidence, we introduce the concept of people reinfectionso Ei > 1→ E1Fig. 2. The effect of population structure on the dynamics of TBdemonstrated in both low and high burden countries. (A): The modelsimulation with population as a limiting factor (SE8I model) and modelwithout population as a limiting factor (SE8I low model) in a low burdencountry. (B): The model with population as a limiting factor (SE8I model)and model without population as a limiting factor (SE8I low model) in a highburden country.Model complexity and parameter derivation: Developingseveral models of increasing complexity in a gradual mannerallowed the parameters to be derived from the simpler models.Fig 3 shows the simulation results for Argentina with differentmodels of various complexity levels and contrast it with theepidemiological data during 20 years.D. ConclusionOur experiment provides a significant evidence that thestructure of population plays a vital role in shaping the dy-namics of the TB. Although simple models could describe thedynamics of the disease, we show that it is necessary to designmore complex model in order to understand some of the morecomplex structure of the TB dynamics. We also showed thatsimple models can provide a significant aid in the estimation ofFig. 3. Comparison of low incidence models fittings for epidemiologicaldata in Argentina.the parameter for more complex models. We finally concludethat the age of the infection and the structure of the latentlyinfected population must to be taken into consideration whiledesigning any TB intervention programREFERENCES[1] W. H. Organization and Others, “Media Centre: Tuberculosis, Fact sheet,”2016.[2] M. R. Nyendak et al., “Mycobacterium tuberculosis SpecificCD8+ T Cells Rapidly Decline with Antituberculosis Treatment,”PLOS ONE, vol. 8, no. 12, pp. 1–10, 2013. [Online]. Available:https://doi.org/10.1371/journal.pone.0081564[3] J.-P. Millet et al., “Predictors of Death among Patients WhoCompleted Tuberculosis Treatment: A Population-Based Cohort Study,”PLOS ONE, vol. 6, no. 9, pp. 1–8, 2011. [Online]. Available:https://doi.org/10.1371/journal.pone.0025315[4] J. Davis et al., “Real-Time Visualization of Mycobacterium-Macrophage Interactions Leading to Initiation of Gran-uloma Formation in Zebrafish Embryos,” Immunity,vol. 17, no. 6, pp. 693–702, 2002. [Online]. Available:http://www.sciencedirect.com/science/article/pii/S1074761302004752[5] K. Bhatt and P. Salgame, “Host Innate Immune Response toMycobacterium tuberculosis,” Journal of Clinical Immunology,vol. 27, no. 4, pp. 347–362, jul 2007. [Online]. Available:https://doi.org/10.1007/s10875-007-9084-0Nura M.R. Ahmad was born in Kano, Nigeria. Hereceives B Sc. degree in Mathematics from BayeroUniversity in 2009, M Sc in Mathematics in 2015from the same university. He joined the depart-ment of physics Universitat Polite`cnica de Catalunya(UPC), Spain, as a Ph.D. student in Sep. 2016, andhis research interest is Complex system modelling.5th BSC Severo Ochoa Doctoral Symposium39

https://upcommons.upc.edu/bitstream/2117/124955/1/14-EFFECT%20OF%20POPULATION.pdf

Effect of population structure, parameter estimation of complex model, and LTBI on TB dynamics

Abstract

Similar works

Full text

Available Versions

UPCommons

UPCommons. Portal del coneixement obert de la UPC