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Article ; Online: SARS-COV-2 outbreak and control in Kenya - Mathematical model analysis.

Mbogo, Rachel Waema / Orwa, Titus Okello

2021 Volume 6, Page(s) 370–380

Abstract: The coronavirus disease 2019 (COVID-19) pandemic reached Kenya in March 2020 with the initial cases reported in the capital city Nairobi and in the coastal area Mombasa. As reported by the World Health Organization, the outbreak of COVID-19 has spread ... ...

Abstract	The coronavirus disease 2019 (COVID-19) pandemic reached Kenya in March 2020 with the initial cases reported in the capital city Nairobi and in the coastal area Mombasa. As reported by the World Health Organization, the outbreak of COVID-19 has spread across the world, killed many, collapsed economies and changed the way people live since it was first reported in Wuhan, China, in the end of 2019. As at the end of December 2020, it had led to over 2.8 million confirmed cases in Africa with over 67 thousand deaths. The trend poses a huge threat to global public health. Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. We employed a SEIHCRD mathematical transmission model with reported Kenyan data on cases of COVID-19 to estimate how transmission varies over time. The model is concise in structure, and successfully captures the course of the COVID-19 outbreak, and thus sheds light on understanding the trends of the outbreak. The next generation matrix approach was adopted to calculate the basic reproduction number (
Language	English
Publishing date	2021-01-27
Publishing country	China
Document type	Journal Article
ZDB-ID	3015225-2
ISSN	2468-0427 ; 2468-2152
ISSN (online)	2468-0427
ISSN	2468-2152
DOI	10.1016/j.idm.2021.01.009
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Optimal control analysis of hepatocytic-erythrocytic dynamics of

Orwa, Titus Okello / Mbogo, Rachel Waema / Luboobi, Livingstone Serwadda

Infectious Disease Modelling

2021 Volume 7, Issue 1, Page(s) 82–108

Abstract: This paper presents an in-host malaria model subject to anti-malarial drug treatment and malaria vaccine antigens combinations. Pontryagin's Maximum Principle is applied to establish optimal control strategies against infected erythrocytes, infected ... ...

Abstract	This paper presents an in-host malaria model subject to anti-malarial drug treatment and malaria vaccine antigens combinations. Pontryagin's Maximum Principle is applied to establish optimal control strategies against infected erythrocytes, infected hepatocytes and malaria parasites. Results from numerical simulation reveal that a combination of pre-erythrocytic vaccine antigen, blood schizontocide and gametocytocide drugs would offer the best strategy to eradicate clinical
Language	English
Publishing date	2021-12-08
Publishing country	China
Document type	Journal Article
ZDB-ID	3015225-2
ISSN	2468-0427 ; 2468-2152
ISSN (online)	2468-0427
ISSN	2468-2152
DOI	10.1016/j.idm.2021.11.006
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article: The

Ngina, Purity / Mbogo, Rachel Waema / Luboobi, Livingstone S

International scholarly research notices

2017 Volume 2017, Page(s) 2124789

Abstract: ... ...

Abstract	The
Language	English
Publishing date	2017-11-14
Publishing country	United States
Document type	Journal Article
ZDB-ID	2778458-7
ISSN	2356-7872
ISSN	2356-7872
DOI	10.1155/2017/2124789
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Multiple-Strain Malaria Infection and Its Impacts on

Orwa, Titus Okello / Mbogo, Rachel Waema / Luboobi, Livingstone Serwadda

Computational and mathematical methods in medicine

2019 Volume 2019, Page(s) 9783986

Abstract: The emergence of parasite resistance to antimalarial drugs has contributed significantly to global human mortality and morbidity due to malaria infection. The impacts of multiple-strain malarial parasite infection have further generated a lot of ... ...

Abstract	The emergence of parasite resistance to antimalarial drugs has contributed significantly to global human mortality and morbidity due to malaria infection. The impacts of multiple-strain malarial parasite infection have further generated a lot of scientific interest. In this paper, we demonstrate, using the epidemiological model, the effects of parasite resistance and competition between the strains on the dynamics and control of
MeSH term(s)	Animals ; Antimalarials/therapeutic use ; Computer Simulation ; Drug Resistance ; Erythrocytes/cytology ; Humans ; Malaria, Falciparum/drug therapy ; Malaria, Falciparum/parasitology ; Medical Informatics ; Models, Theoretical ; Mosquito Vectors ; Plasmodium falciparum/drug effects ; Plasmodium falciparum/genetics ; Research Design ; Species Specificity
Chemical Substances	Antimalarials
Language	English
Publishing date	2019-06-11
Publishing country	United States
Document type	Journal Article
ZDB-ID	2252430-7
ISSN	1748-6718 ; 1748-670X ; 1027-3662
ISSN (online)	1748-6718
ISSN	1748-670X ; 1027-3662
DOI	10.1155/2019/9783986
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Modelling Optimal Control of In-Host HIV Dynamics Using Different Control Strategies.

Ngina, Purity / Mbogo, Rachel Waema / Luboobi, Livingstone S

Computational and mathematical methods in medicine

2018 Volume 2018, Page(s) 9385080

Abstract: HIV is one of the major causes of deaths, especially in Sub-Saharan Africa. In this paper, an in vivo deterministic model of differential equations is presented and analyzed for HIV dynamics. Optimal control theory is applied to investigate the key roles ...

Abstract	HIV is one of the major causes of deaths, especially in Sub-Saharan Africa. In this paper, an in vivo deterministic model of differential equations is presented and analyzed for HIV dynamics. Optimal control theory is applied to investigate the key roles played by the various HIV treatment strategies. In particular, we establish the optimal strategies for controlling the infection using three treatment regimes as the system control variables. We have applied Pontryagin's Maximum Principle in characterizing the optimality control, which then has been solved numerically by applying the Runge-Kutta forth-order scheme. The numerical results indicate that an optimal controlled treatment strategy would ensure significant reduction in viral load and also in HIV transmission. It is also evident from the results that protease inhibitor plays a key role in virus suppression; this is not to underscore the benefits accrued when all the three drug regimes are used in combination.
MeSH term(s)	Antiviral Agents/therapeutic use ; HIV Infections/drug therapy ; HIV Infections/virology ; Humans ; Models, Theoretical ; Viral Load
Chemical Substances	Antiviral Agents
Language	English
Publishing date	2018-06-04
Publishing country	United States
Document type	Journal Article
ZDB-ID	2252430-7
ISSN	1748-6718 ; 1748-670X ; 1027-3662
ISSN (online)	1748-6718
ISSN	1748-670X ; 1027-3662
DOI	10.1155/2018/9385080
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Modelling Optimal Control of In-Host HIV Dynamics Using Different Control Strategies

Purity Ngina / Rachel Waema Mbogo / Livingstone S. Luboobi

Computational and Mathematical Methods in Medicine, Vol

2018 Volume 2018

Abstract	HIV is one of the major causes of deaths, especially in Sub-Saharan Africa. In this paper, an in vivo deterministic model of differential equations is presented and analyzed for HIV dynamics. Optimal control theory is applied to investigate the key roles played by the various HIV treatment strategies. In particular, we establish the optimal strategies for controlling the infection using three treatment regimes as the system control variables. We have applied Pontryagin’s Maximum Principle in characterizing the optimality control, which then has been solved numerically by applying the Runge-Kutta forth-order scheme. The numerical results indicate that an optimal controlled treatment strategy would ensure significant reduction in viral load and also in HIV transmission. It is also evident from the results that protease inhibitor plays a key role in virus suppression; this is not to underscore the benefits accrued when all the three drug regimes are used in combination.
Keywords	Computer applications to medicine. Medical informatics ; R858-859.7
Subject code	531
Language	English
Publishing date	2018-01-01T00:00:00Z
Publisher	Hindawi Limited
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Multiple-Strain Malaria Infection and Its Impacts on Plasmodium falciparum Resistance to Antimalarial Therapy

Titus Okello Orwa / Rachel Waema Mbogo / Livingstone Serwadda Luboobi

Computational and Mathematical Methods in Medicine, Vol

A Mathematical Modelling Perspective

2019 Volume 2019

Abstract	The emergence of parasite resistance to antimalarial drugs has contributed significantly to global human mortality and morbidity due to malaria infection. The impacts of multiple-strain malarial parasite infection have further generated a lot of scientific interest. In this paper, we demonstrate, using the epidemiological model, the effects of parasite resistance and competition between the strains on the dynamics and control of Plasmodium falciparum malaria. The analysed model has a trivial equilibrium point which is locally asymptotically stable when the parasite’s effective reproduction number is less than unity. Using contour plots, we observed that the efficacy of antimalarial drugs used, the rate of development of resistance, and the rate of infection by merozoites are the most important parameters in the multiple-strain P. falciparum infection and control model. Although the drug-resistant strain is shown to be less fit, the presence of both strains in the human host has a huge impact on the cost and success of antimalarial treatment. To reduce the emergence of resistant strains, it is vital that only effective antimalarial drugs are administered to patients in hospitals, especially in malaria-endemic regions. Our results emphasize the call for regular and strict surveillance on the use and distribution of antimalarial drugs in health facilities in malaria-endemic countries.
Keywords	Computer applications to medicine. Medical informatics ; R858-859.7
Subject code	572
Language	English
Publishing date	2019-01-01T00:00:00Z
Publisher	Hindawi Limited
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: The In Vivo Dynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells

Purity Ngina / Rachel Waema Mbogo / Livingstone S. Luboobi

International Scholarly Research Notices , Vol

2017 Volume 2017

Abstract: The in vivo dynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system ... ...

Abstract	The in vivo dynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having R0<1. Lastly, the biological dynamics of HIV in vivo infection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral replication. In addition, the results emphasize the importance of developing controls, interventions, and management policies that when implemented would lead to viral suppression during acute infection.
Keywords	Technology ; T ; Science ; Q
Subject code	570
Language	English
Publishing date	2017-01-01T00:00:00Z
Publisher	Hindawi Publishing Corporation
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Mathematical model for the in-host malaria dynamics subject to malaria vaccines

Titus Okello Orwa / Rachel Waema Mbogo / Livingstone Serwadda Luboobi

Letters in Biomathematics, Vol 5, Iss 1, Pp 222-

2018 Volume 251

Abstract: Despite the success of the existing malaria control strategies, reported malaria cases are still quite high. In 2016, the WHO reported about 216 million malaria cases; 90% of which occurred in the WHO African Region. In this paper, a mathematical model ... ...

Abstract	Despite the success of the existing malaria control strategies, reported malaria cases are still quite high. In 2016, the WHO reported about 216 million malaria cases; 90% of which occurred in the WHO African Region. In this paper, a mathematical model for the in-host Plasmodium falciparum malaria subject to malaria vaccines is formulated and analysed. An efficacious pre-erythrocytic vaccine is shown to greatly reduce the severity of clinical malaria. Based on the normalized forward sensitivity index technique, the average number of merozoites released per bursting blood schizont is shown to be the most sensitive parameter in the model. Numerical simulation results further suggest that an efficacious blood stage vaccine has the potential to reduce the burst size of the blood schizonts and maximize the rate of activation of CD8+ T cells during malaria infection. Moreover, vaccine combinations that are efficacious might help in achieving a malaria free population by the year 2030. This paper provides useful insights in malaria vaccine control and a unique opportunity to intensify support and funding for malaria vaccine development.
Keywords	Malaria vaccines ; vaccine efficacy ; hepatocytes ; CD8+ T cells ; red blood cells ; Plasmodium falciparum ; Biology (General) ; QH301-705.5 ; Mathematics ; QA1-939
Subject code	616
Language	English
Publishing date	2018-12-01T00:00:00Z
Publisher	Intercollegiate Biomathematics Alliance
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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