In-host density-dependent model of high-risk HPV virions, basal cells, lymphocytes t-cells incorporating functional responses

Sep 21, 2026

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Cervical cancer is a major malignancy largely driven by high-risk human papillomavirus (HPV), whose spread and within-host dynamics require improved mathematical descriptions. The study develops an in-host density-dependent deterministic model for basal cells, virions, and lymphocytes, explicitly incorporating immunity and functional responses. Six compartments—susceptible cells, infected cells, precancerous cells, cancerous cells, virions, and lymphocytes—are analyzed using epidemiological modeling tools. Basic reproduction number R0 is derived via next generation matrix, survival function, and a characteristic polynomial approach. Stability analysis shows a disease-free equilibrium that is locally asymptotically stable when R0*<1 and globally asymptotically stable when R0*≤1, while the endemic equilibrium is globally asymptotically stable for R0*>1.

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Introduction

Heliyon 10 (2024) e35038 Contents lists available at ScienceDirect Heliyon journal [homepage:](homepage: www.cell.com/heliyon)[ www.cell.com/heliyon](homepage: www.cell.com/heliyon) | Research article
In-host density-dependent model of high-risk HPV virions, basal cells, lymphocytes t-cells incorporating functional responses
Elosy Makenaa, * , Cyrus Gitonga Ngarib , Patrick Mwangi Kimania , Jeremiah Savali Kilonzic
a Department of Mathematics and Statistics, University of Embu, 6-60100 Embu, Kenya b Department of Pure and Applied Sciences, Kirinyaga University, 143-10300 Kerugoya, Kenya c Department of Mathematics, Meru University of Science and Technology, 972-60200 Meru, Kenya | | | | --- | --- | --- | | A R T I C L E I N F O | | A B S T R A C T | | Keywords:
In-host model Functional responses Stability analysis
Simulation and reproduction number | | Cervical cancer is one of the most common types of cancer and it is caused mostly by high-risk Human Papillomavirus (HPV) and continues to spread at an alarming rate. While HPV impacts have been investigated before, there are currently only a scanty number of mathematical models that account for HPV′s dynamic role in cervical cancer. The objectives were to develop an in-host density-dependent deterministic model for the dynamics implications of basal cells, virions, and lymphocytes incorporating immunity and functional responses. Analyze the model using techniques of epidemiological models such as basic reproduction number and simulate the model using Matlab ODE solver. Six compartments are considered in the model that is; Susceptible cells (S), Infected cells (I), Precancerous cells (P), Cancerous cells (C), Virions (V), and Lymphocytes (L). Next generation matrix (NGM), survival function, and characteristic polynomial method were used to determine the basic reproduction number denoted as R0 . R0 was obtained using three methods because NGM has some weaknesses hence the need for the other two methods. The findings from this research indicated that Disease-Free Equilibrium point is locally asymptotically stable whenever R*0 < 1 and globally asymptotically stable if R*0 ≤ 1 and the Endemic Equilibrium is globally asymptotically stable if R*0 > 1. The results obtained shows that the progression rate of precancerous cells to cancerous cells (θ) has the most direct impact on the model. The model was able to estimate the longevity of a patient as 10 days when (θ) increases by 0.08. The findings of this research will help healthcare providers, public health authorities, and non-governmental health groups in creating effective prevention strategies to slow the development of cervical cancer. More research should be done to determine the exact number of cancerous cells that can lead to the death of a cervical cancer patient since this paper estimated a proportion of 75%. | 1. Introduction According to Ref. [1], cervical cancer arises from the uncontrolled, invasive proliferation of epithelial cells in the cervix, the area of the uterus that attaches to the vagina. Human Papillomavirus (HPV) is the main cause of cervical cancer, and in over 90 % of instances, * Corresponding author. E-mail addresses: [elseakesh@gmail.com](elseakesh@gmail.com) (E. Makena), [ngaricyrus15@gmail.com](ngaricyrus15@gmail.com) (C.G. Ngari), [patkim32@gmail.com](patkim32@gmail.com) (P.M. Kimani), [jeremiahkilonzi66@gmail.com](jeremiahkilonzi66@gmail.com) (J.S. Kilonzi). [https://doi.org/10.1016/j.heliyon.2024.e35038](https://doi.org/10.1016/j.heliyon.2024.e35038) Received 16 February 2024; Received in revised form 6 July 2024; Accepted 22 July 2024 Available online 25 July 2024 2405-8440/© 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ([http://creativecommons.org/licenses/by-nc-nd/4.0/](http://creativecommons.org/licenses/by-nc-nd/4.0/)). HPV infection contributes to the development of cancer [1]. Small double-s

FAQs

What does the model include in terms of biological compartments?

It considers six compartments: susceptible cells (S), infected cells (I), precancerous cells (P), cancerous cells (C), virions (V), and lymphocytes (L).

How is the basic reproduction number R0 determined in the paper?

R0 is computed using the next generation matrix, survival function, and the characteristic polynomial method, with three approaches used because the next generation matrix has limitations.

What stability conditions are reported for the disease-free and endemic equilibria?

The disease-free equilibrium is locally asymptotically stable when R0*<1 and globally asymptotically stable when R0*≤1; the endemic equilibrium is globally asymptotically stable when R0*>1.

Sep 21, 2026

Uploaded by Theodore