Browsing by Author "Shaban, Nyimvua"

Now showing 1 - 8 of 8
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    Formulation of Mathematical Model for TB Transmission in Zoonotic Areas with Existence of Endemic Equilibrium
    (Scientific Research Publishing, 2014) Mwenyeheri, Thomas; Shaban, Nyimvua; Hove-Msekwa, Doroth; Chibaya, Symon B.; Ngadaya, Esther; Mfinanga, Sayoki
    A mathematical model incorporating animal TB and Human TB transmission is formulated and analysed in order to determine the role of animal TB and human TB in the overall TB transmission and also, to determine the parameters which govern the transmission of the TB disease. The model has five classes namely susceptible, exposed animal TB, and exposed human TB, infectious and recovery. The model assumed that there are two classes for infected individuals, those who acquired TB through animal and those who acquire TB from human. Qualitative results show that the model has the disease-free equilibrium and at least one endemic equilibrium that is locally asymptotically stable. The study includes numerical simulations as a way of supporting the analytical results. Graphical results indicate that animal TB has major contribution on overall TB transmission and the TB transmission can be reduced by ensuring intervention to both Animal TB and Human TB. Furthermore the equations indicate that there is at least one endemic equilibrium which translates that t animal and human have the contribution on TB transmission. This shows that both animals and humans together with fast progressors have contribution on TB transmissions.
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    Household Epidemics: Modelling Effects of Early Stage Vaccination
    (Wiley, 2009) Shaban, Nyimvua; Andersson, Mikael; Svensson, Åke; Britton, Tom
    A Markovian susceptible - infectious - removed (SIR) epidemic model is considered in a community partitioned into households. A vaccination strategy, which is implemented during the early stages of the disease following the detection of infected individuals is proposed. In this strategy, the detection occurs while an individual is infectious and other susceptible household members are vaccinated without further delay. Expressions are derived for the influence on the reproduction numbers of this vaccination strategy for equal and unequal household sizes. We fit previously estimated parameters from influenza and use household distributions for Sweden and Tanzania census data. The results show that the reproduction number is much higher in Tanzania (6 compared with 2) due to larger households, and that infected individuals have to be detected (and household members vaccinated) after on average 5 days in Sweden and after 3.3 days in Tanzania, a much smaller difference.
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    Modelling the Effects of Public Health Education in the Spread of Hepatitis B Disease
    (2015) Shaban, Nyimvua
    This paper presents a mathematical model that captures some essential dynamics of Hepatitis B transmission to study the impacts of public health educational campaign in preventing the disease. The educational induced reproduction number Re is compared with the basic reproduction number R0 to assess the possible benefits to be obtained from this control measure. Numerical results and sensitivity analysis are carried out to support the analytical results and determine the parameters in- fluencing the dynamics of the disease. It is indicated that in the presence of public health education campaign, transmission of infection decreases when people are aware of the disease, implying that the number of acute and chronic infected individuals decrease as well.
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    Modelling the Impact of Vaccination and Screening on the Dynamics of Human Papillomavirus Infection
    (2014) Shaban, Nyimvua; Mofi, Hawa
    While human papillomavirus has been a recognized disease for a long time, the control of outbreaks remains a challenge. The aim of this study is to investigate the role of screening and vaccination as control strategies in curtailing the spread of the disease. Using the next generation matrix, the disease free equilibrium has be shown to be asymptotically stable. Furthermore, sensitivity analysis is then performed on the key parameters driving HPV dynamics in order to detrmine their relative importance and potential impact in HPV dynamics and to dertmine the impacts of vaccination and screening in the spread of HPV. Numerical results indicate that HPV infection can be reduced hwn both interventions, that is screenig and vaccination, are implemented in order to reduce the burden of the disease.
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    Network Epidemics and Early Stage Vaccination: The Effects of Infectious and Vaccination Delay Periods and Their Randomness
    (2011) Shaban, Nyimvua; Andersson, Mikael; Svensson, Åke; Britton, Tom
    It is known that the distributions of the latent and infectious periods affect the dynamics of the spread of an infectious disease. Here we consider the SEIR epidemic model describing the spread of an infectious disease giving life-long immunity in a community whose social structure can be represented by a simple random graph having a pre-specified degree distribution. Two real time vaccination strategies, based on tracing and vaccinating the friends of infectious individuals during the early stages of an epidemic, are proposed. The first strategy considers vaccination of each friend of a detected infectious individual independently with probability ρ. The second strategy sets an upper bound on the number of friends an individual can infect before being detected. We derive both the basic reproduction number and the strategy-specific reproduction numbers and show that these reproduction numbers decrease when the variances of the infectious period and the time to detection increase. Under the assumption that detection may only occur after the latent period, the reproduction numbers are independent of the distribution of the latent period.
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    Networks, Epidemics and Vaccination through Contact Tracing
    (Elsevier, 2008) Shaban, Nyimvua; Andersson, Mikael; Svensson, Åke; Britton, Tom
    We consider a (social) network whose structure can be represented by a simple random graph having a pre-specified degree distribution. A Markovian SIR epidemic model is defined on such a social graph. We then consider two real-time vaccination models for contact tracing during the early stages of an epidemic outbreak. The first model considers vaccination of each friend of an infectious individual (once identified) independently with probability ρ. The second model is related to the first model but also sets a bound on the maximum number an infectious individual can infect before being identified. Expressions are derived for the influence on the reproduction number of these vaccination models. We give some numerical examples and simulation results based on the Poisson and heavy-tail degree distributions where it is shown that the second vaccination model has a bigger advantage compared to the first model for the heavy-tail degree distribution.
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    Optimal Control of a Threatened Wildebeest-Lion Prey-Predator System in the Serengeti Ecosystem
    (Scientific Research Publishing, 2015-04-01) Sagamiko, T. D.; Shaban, Nyimvua; Nahonyo, C. L.; Makinde, O. D.
    We develop a two-species prey-predator model in which prey is wildebeest and predator is lion. The threats to wildebeest are poaching and drought while to lion are retaliatory killing and drought. The system is found in the Serengeti ecosystem. Optimal control theory is applied to investigate optimal strategies for controlling the threats in the system where anti-poaching patrols are used for poaching, construction of strong bomas for retaliatory killing and construction of dams for drought control. The possible impact of using a combination of the three controls either one at a time or two at a time on the threats facing the system is also examined. We observe that the best result is achieved by using all controls at the same time, where a combined approach in tackling threats to yield optimal results is a good approach in the management of wildlife populations.
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    The Use of Non-Standard Finite Difference Schemes to Solve the DAMP and SIT Models
    (Science and Education Publishing, 2016-01-15) Mwasunda, Joshua A.; Mureithi, Eunice W.; Shaban, Nyimvua
    Sterile insect technique (SIT) is a method of biological control that uses sterile male insects to reduce the reproductive rate of a species of target insect. The method relies on the release of sterile or treated males in order to reduce the native population of insects. We propose the model that governs the dynamics of the anopheles mosquito population, and then modify to incorporate the sterile insect technique as an intervention to curtail the reproduction of mosquitoes. The nonstandard finite difference numerical schemes and simulations for these models are provided. The results indicate that sterile technique with frequent and high rate of release can be an alternative to chemical control tools in the fight against malaria.