Date of Publication
8-18-2026
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Subject Categories
Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics Department
Thesis Advisor
Ederlina G. Nocon
Defense Panel Chair
Angelyn R. Lao
Defense Panel Member
Severino V. Gervacio
Yvette F. Lim
Daryl Q. Granario
Gaudencio C. Petalcorin, Jr.
Abstract (English)
Population growth processes have long been studied in population theory, epidemiology, branching processes, and matrix population models. Existing formulations capture various forms of growth, transmission, and decline, but often focus on homogeneous populations, stochastic dynamics, aggregate representations, or specialized attrition mechanisms. In particular, the literature reviewed does not appear to contain recursive population models that simultaneously incorporate recursive prime-agent replication, generation-dependent exposure parameters, generation-dependent success ratios, and structured attrition mechanisms within a unified deterministic framework. This dissertation addresses this gap by developing a generalized iterative prime-agent model that integrates recursive growth, heterogeneous transmission dynamics, and multiple attrition structures within a common mathematical framework. Although the multi-class extension is expressed through matrices, the framework differs from Leslie-type matrix population models: rather than beginning with empirically specified fertility, survival, and stage-transition rates, it begins with success-driven recursive replication and explicit deterministic attrition rules.
The study develops recursive formulations describing the interaction between replication and attrition under varying structural assumptions. The proposed framework incorporates heterogeneous generation-dependent exposure parameters, heterogeneous success ratios, and multi-class recursive interactions within a discrete deterministic setting. Here, a class denotes a distinct prime-agent category, and interclass recruitment is governed by specified transition proportions. Single-class generational systems and multi-class matrix-recursive systems are developed together with proportional attrition, constant attrition, and finite-lifespan removal mechanisms. Recursive, combinatorial, and matrix-based formulations are derived, including closed-form representations and matrix-recursive and matrix-polynomial structures for multi-class systems.
The results show that the generalized framework places several recursive prime-agent formulations within a common mathematical structure. Under appropriate homogeneous assumptions, the generalized models recover earlier recursive prime-agent models as special cases. The analysis further reveals threshold relationships governing the interaction between growth and attrition and, in the finite-lifespan setting, produces delayed correction effects associated with Pascal-type and inclusion-exclusion coefficient patterns. These results provide a common mathematical framework for analyzing recursive population growth and attrition across a range of heterogeneous and multi-class systems.
The resulting framework extends the study of discrete deterministic growth systems with structured attrition and provides a foundation for further analytical, computational, stochastic, and nonlinear investigations involving recursive transmission and population processes in organizational, social, and ecological settings.
Abstract Format
html
Abstract (Filipino)
Matagal nang pinag-aaralan ang mga proseso ng paglago ng populasyon sa teorya ng populasyon, epidemiolohiya, branching processes, at matrix population models. Nailalarawan ng mga umiiral na pormulasyon ang iba’t ibang anyo ng paglago, transmisyon, at pagbaba, ngunit kadalasan ay nakatuon ang mga ito sa homogeneous na populasyon, stochastic dynamics, aggregate representations, o mga espesyalisadong mekanismo ng attrition. Sa partikular, batay sa sinuring literatura, hindi lumilitaw na may recursive population models na sabay-sabay na nagsasama ng recursive prime-agent replication, generation-dependent exposure parameters, generation-dependent success ratios, at structured attrition mechanisms sa loob ng isang pinag-isang deterministic framework. Tinutugunan ng disertasyong ito ang puwang na ito sa pamamagitan ng pagbuo ng isang generalized iterative prime-agent model na nagsasama ng recursive growth, heterogeneous transmission dynamics, at iba’t ibang attrition structures sa loob ng iisang mathematical framework. Bagama’t ipinapahayag ang multi-class extension sa pamamagitan ng mga matrix, naiiba ang framework na ito sa Leslie-type matrix population models: sa halip na magsimula sa empirically specified fertility, survival, at stage-transition rates, nagsisimula ito sa success-driven recursive replication at tahasang itinakdang deterministic attrition rules.
Bumubuo ang pag-aaral ng mga recursive formulation na naglalarawan sa ugnayan ng replication at attrition sa ilalim ng iba’t ibang structural assumptions. Isinasama ng iminungkahing framework ang heterogeneous generation-dependent exposure parameters, heterogeneous success ratios, at multi-class recursive interactions sa loob ng isang discrete deterministic setting. Dito, ang isang class ay tumutukoy sa isang natatanging kategorya ng prime-agent, at ang interclass recruitment ay pinamamahalaan ng mga itinakdang transition proportions. Binubuo ang single-class generational systems at multi-class matrix-recursive systems kasama ang proportional attrition, constant attrition, at finite-lifespan removal mechanisms. Hinango ang mga recursive, combinatorial, at matrix-based na pormulasyon, kabilang ang closed-form representations at matrix-recursive at matrix-polynomial structures para sa multi-class systems.
Ipinakikita ng mga resulta na inilalagay ng generalized framework ang ilang recursive prime-agent formulations sa loob ng iisang mathematical structure. Sa ilalim ng naaangkop na homogeneous assumptions, naibabalik ng generalized models ang mga naunang recursive prime-agent models bilang mga special case. Ipinakikita rin ng pagsusuri ang mga threshold relationships na namamahala sa ugnayan ng growth at attrition at, sa finite-lifespan setting, lumilitaw ang mga delayed correction effects na kaugnay ng Pascal-type at inclusion–exclusion coefficient patterns. Nagbibigay ang mga resultang ito ng isang pinag-isang mathematical framework para sa pagsusuri ng recursive population growth at attrition sa iba’t ibang heterogeneous at multi-class systems.
Pinalalawak ng nabuong framework ang pag-aaral ng discrete deterministic growth systems na may structured attrition at nagbibigay ng pundasyon para sa mga susunod pang analytical, computational, stochastic, at nonlinear na pag-aaral na may kinalaman sa recursive transmission at population processes sa organizational, social, at ecological settings.
Abstract Format
html
Language
English
Format
Electronic
Keywords
Iterative methods (Mathematics); Mathematical models
Recommended Citation
Wee, A. A. (2026). A generalized iterative prime-agent model with structured attrition. Retrieved from https://animorepository.dlsu.edu.ph/etdd_math/8
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Embargo Period
8-18-2028
