A Mathematical Model for the Within-Host Dynamics of Malaria Parasite with Adaptive Immune Responses
Mathematical analysis of epidemics is crucial for long-term disease prediction and helps to guide decision-makers in terms of public health policy. In this study, we develop a within-host mathematical model of the malaria parasite dynamics with the effect of an adaptive immune response. The model in...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2024/6667262 |
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| author | Jemal Muhammed Ahmed Getachew Tashome Tilahun Shambel Tadesse Degefa |
| author_facet | Jemal Muhammed Ahmed Getachew Tashome Tilahun Shambel Tadesse Degefa |
| author_sort | Jemal Muhammed Ahmed |
| collection | DOAJ |
| description | Mathematical analysis of epidemics is crucial for long-term disease prediction and helps to guide decision-makers in terms of public health policy. In this study, we develop a within-host mathematical model of the malaria parasite dynamics with the effect of an adaptive immune response. The model includes six compartments, namely, the uninfected red blood cells, infected red blood cells, merozoites, gametocytes, cytotoxic T cells immune response, and antibodies immune response, which are activated in the host to attack the parasite. We establish the well-posedness and biological feasibility of the model in terms of proving the non-negativity and boundedness of solutions. The most important threshold value in the epidemiological model known as the basic reproduction number, R0, which is used to determine the stability of the steady state, is investigated. Furthermore, the parasite-free equilibrium is locally and globally stable if the basic reproduction number, R0<1, otherwise, if R0>1, then there exist four parasite-persistence equilibria. The stability conditions of these parasite-persistence equilibria are presented. Sensitivity analysis of the basic reproduction number shows that parameters representing the recruitment rate of uninfected red blood cells, infection rate of red blood cells by merozoites, and the average number of merozoites per ruptured infected red blood cells are the most influential ones in affecting the dynamics. Finally, several numerical simulations of the model are presented to supplement the theoretical and analytical findings. It has been observed that numerical simulations and theoretical results are coherent. The response of cytotoxic T cells and antibodies has a significant impact on suppressing infected cells and malaria parasites in the host’s body. |
| format | Article |
| id | doaj-art-f7b98a24f26a4fb4aa8d41cbc336e7b9 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f7b98a24f26a4fb4aa8d41cbc336e7b92025-02-03T11:21:06ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252024-01-01202410.1155/2024/6667262A Mathematical Model for the Within-Host Dynamics of Malaria Parasite with Adaptive Immune ResponsesJemal Muhammed Ahmed0Getachew Tashome Tilahun1Shambel Tadesse Degefa2Adama Science and Technology UniversityHaramaya UniversityAdama Science and Technology UniversityMathematical analysis of epidemics is crucial for long-term disease prediction and helps to guide decision-makers in terms of public health policy. In this study, we develop a within-host mathematical model of the malaria parasite dynamics with the effect of an adaptive immune response. The model includes six compartments, namely, the uninfected red blood cells, infected red blood cells, merozoites, gametocytes, cytotoxic T cells immune response, and antibodies immune response, which are activated in the host to attack the parasite. We establish the well-posedness and biological feasibility of the model in terms of proving the non-negativity and boundedness of solutions. The most important threshold value in the epidemiological model known as the basic reproduction number, R0, which is used to determine the stability of the steady state, is investigated. Furthermore, the parasite-free equilibrium is locally and globally stable if the basic reproduction number, R0<1, otherwise, if R0>1, then there exist four parasite-persistence equilibria. The stability conditions of these parasite-persistence equilibria are presented. Sensitivity analysis of the basic reproduction number shows that parameters representing the recruitment rate of uninfected red blood cells, infection rate of red blood cells by merozoites, and the average number of merozoites per ruptured infected red blood cells are the most influential ones in affecting the dynamics. Finally, several numerical simulations of the model are presented to supplement the theoretical and analytical findings. It has been observed that numerical simulations and theoretical results are coherent. The response of cytotoxic T cells and antibodies has a significant impact on suppressing infected cells and malaria parasites in the host’s body.http://dx.doi.org/10.1155/2024/6667262 |
| spellingShingle | Jemal Muhammed Ahmed Getachew Tashome Tilahun Shambel Tadesse Degefa A Mathematical Model for the Within-Host Dynamics of Malaria Parasite with Adaptive Immune Responses International Journal of Mathematics and Mathematical Sciences |
| title | A Mathematical Model for the Within-Host Dynamics of Malaria Parasite with Adaptive Immune Responses |
| title_full | A Mathematical Model for the Within-Host Dynamics of Malaria Parasite with Adaptive Immune Responses |
| title_fullStr | A Mathematical Model for the Within-Host Dynamics of Malaria Parasite with Adaptive Immune Responses |
| title_full_unstemmed | A Mathematical Model for the Within-Host Dynamics of Malaria Parasite with Adaptive Immune Responses |
| title_short | A Mathematical Model for the Within-Host Dynamics of Malaria Parasite with Adaptive Immune Responses |
| title_sort | mathematical model for the within host dynamics of malaria parasite with adaptive immune responses |
| url | http://dx.doi.org/10.1155/2024/6667262 |
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