Doctoral Degrees (Applied Mathematics)

Permanent URI for this collectionhttps://hdl.handle.net/10413/7094

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Analysis of multiple control strategies for pre-exposure prophylaxis and post-infection interventions on HIV infection.
(2016) Afassinou, Komi.; Chirove, Faraimunashe.; Govinder, Keshlan Sathasiva.
Abstract available in PDF file.
Epidemiological modelling of foot and mouth disease control in cattle: incorporating time and spatial spread of disease dynamics.
(2019) Tessema, Kassahun Mengist.; Chirove, Faraimunashe.; Sibanda, Precious.
Foot and mouth disease (FMD) is a contagious animal viral infection that can spread rapidly if the disease is not monitored and controlled. Therefore, protecting livestock and controlling foot and mouth disease is important for preventing economic losses. Much of the global burden of economic losses due to foot and mouth disease falls on the worlds poorest countries that mostly depend upon the health of their livestock. In these countries, the availability of FMD also has an impact on the overall herd fertility, modifying the herd structure and affecting the selection of breeds. Modelling the dynamics of FMD using mathematical analysis and simulations can assist to monitor and control the spread of the disease. In this thesis, we develop, study, and analyse models of foot and mouth disease in cattle by incorporate vaccination that does not induce rapid protection, time delays, both time and spatial spread with different control strategies. The results show that even though vaccines may not induce rapid protection the combining of a high rate of vaccination and low loss of vaccine protection rate may be successful in reducing the foot and mouth burden provided critical vaccination thresholds are taken into consideration. The results also show that control strategies play a significant role in moving the animals into protected routes of infection than leaving more animals into the unprotected route of infection. We also capture the effects of prophylactic vaccination, reactive vaccination, prophylactic treatment, reactive culling and the effects of time delay. The results of foot and mouth disease with two-time delays show that the burden of infection decreases significantly when unprotected animals delay maximally their time to show clinical symptoms, and at the same time by increasing the effectiveness of the control strategies. The study also explores the effects of spatial diffusion, quarantine of clinically infected animals and shedding of foot and mouth disease virus into the environment. Analysis of foot and mouth disease control models suggests that implementing of an effective combination of control strategies, limiting the movement of susceptible animals and the shedding of FMDV protects animals from foot and mouth disease burden.
Mathematical modelling of the Ebola virus disease.
(2024) Abdalla, Suliman Jamiel Mohamed.; Govinder, Keshlan Sathasiva.; Chirove, Faraimunashe.
Despite the numerous modelling efforts to advise public health physicians to understand the dynamics of the Ebola virus disease (EVD) and control its spread, the disease continued to spread in Africa. In the current thesis, we systematically review previous EVD models. Further, we develop novel mathematical models to explore two important problems during the 2018-2020 Kivu outbreak: the impact of geographically targeted vaccinations (GTVs) and the interplay between the attacks on Ebola treatment centres (ETCs) and the spread of EVD. In our systematic review, we identify many limitations in the modelling literature and provide brief suggestions for future work. Our modelling findings underscore the importance of considering GTVs in areas with high infections. In particular, we find that implementing GTVs in regions with high infections so that the total vaccinations are increased by 60% decreases the cumulative cases by 15%. On the other hand, we need to increase the vaccinations to more than 1000% to achieve the 15% decrease in EVD cases if we implement GTVs in areas with low infections. On the impact of the attacks on ETCs, we find that due to the attacks on ETCs, the cumulative cases increased by more than 17% during the 2018-2020 Kivu outbreak. We also find that when 10% of the hospitalised individuals flee the attacks on ETCs after spending only three days under treatment, the cumulative cases increased by more than 30% even if these individuals all returned to the ETCs three days later. On the other hand, if only half of these individuals returned to ETCs for treatment, the cumulative cases increase by approximately 50%. Further, when these patients spend one more day in the community, after which they all return to ETCs, the cumulative cases rise by an additional 10%. Global sensitivity analysis also confirmed these findings. To conclude, our literature systematic review is used to identify many critical factors which were overlooked in previous EVD models. Our modelling findings show that the attacks on ETCs can be destructive to the efforts of EVD response teams. Hence, it is important for decision-makers to tackle the reasons for community distrust and address the roots of the hostility towards ETCs. We also find that GTVs can be used to contain the spread of EVD when ring vaccinations, contact tracing and antiviral treatments cannot successfully control the spread of EVD.
Using epidemiological mathematical models to understand the transmission dynamics of bovine tuberculosis in buffalo and cattle populations.
(2015) Phepha, Patrick B.; Chirove, Faraimunashe.; Govinder, Keshlan Sathasiva.
In South Africa, buffalo are the maintenance hosts of Mycobacterium bovis (M. bovis), a pathogen that causes bovine tuberculosis in wildlife and domesticated animals. To understand the transmission dynamics of M. bovis, mathematical epidemiological models are developed. The models address various questions about the transmission dynamics of bovine tuberculosis in both buffalo and cattle populations. The key questions addressed by the models are: can buffalo carriers fuel the re-occurance of bovine tuberculosis in buffalo population? Is the cross- infection transmission route responsible for the persistence of bovine tuberculosis in cattle population? Can the movement of buffalo from one patch to another be the reason for the spread of bovine tuberculosis in Kruger National Park? These questions are addressed in Chapters 2, 3 and 4 respectively. Both the mathematical and numerical analysis suggest that the infection parameters associated with buffalo carriers and cross-infection and movement parameters associated with the movement of susceptible and exposed buffalo from one patch to another are among the key drivers of bovine tuberculosis in buffalo and cattle populations. The findings have very vital implications for bovine tuberculosis control. If bovine tuberculosis is to be eliminated, there is need to develop tests that can detect buffalo carriers from buffalo population. This will accelerate the eradication of bovine tuberculosis (BTB) infection from the buffalo population. Measures need to be taken to prevent the mixing of cattle and buffalo populations at the interface and also restrict the movement of bufffalo from one patch to another in Kruger National Park.

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Browsing Doctoral Degrees (Applied Mathematics) by Author "Chirove, Faraimunashe."