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- Nicolas Bacaër, Rachid Ouifki, Carel Pretorius, Robin Wood, Brian Williams
- Journal of mathematical biology
- 2008

We present a simple mathematical model with six compartments for the interaction between HIV and TB epidemics. Using data from a township near Cape Town, South Africa, where the prevalence of HIV is above 20% and where the TB notification rate is close to 2,000 per 100,000 per year, we estimate some of the model parameters and study how various control… (More)

- Kazeem O. Okosun, Rachid Ouifki, Nizar Marcus
- Biosystems
- 2011

We derive and analyse a deterministic model for the transmission of malaria disease with mass action form of infection. Firstly, we calculate the basic reproduction number, R(0), and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation. The implication of this occurrence is that the classical… (More)

- Nicolas Bacaër, Rachid Ouifki
- Mathematical biosciences
- 2007

For continuous-time population models with a periodic factor which is sinusoidal, both the growth rate and the basic reproduction number are shown to be the largest roots of simple equations involving continued fractions. As an example, we reconsider an SEIS model with a fixed latent period, an exponentially distributed infectious period and a sinusoidal… (More)

- Kazeem O. Okosun, Rachid Ouifki, Nizar Marcus
- Biosystems
- 2013

The aim of this paper is to investigate the effectiveness and cost-effectiveness of three malaria preventive measures (use of treated bednets, spray of insecticides and a possible treatment of infective humans that blocks transmission to mosquitoes). For this, we consider a mathematical model for the transmission dynamics of the disease that includes these… (More)

- John W. Hargrove, Rachid Ouifki, Damian Kajunguri, Glyn A. Vale, Stephen J. Torr
- PLoS neglected tropical diseases
- 2012

BACKGROUND
In Uganda, Rhodesian sleeping sickness, caused by Trypanosoma brucei rhodesiense, and animal trypanosomiasis caused by T. vivax and T. congolense, are being controlled by treating cattle with trypanocides and/or insecticides. We used a mathematical model to identify treatment coverages required to break transmission when host populations… (More)

- Damian Kajunguri, John W Hargrove, Rachid Ouifki, J Y T Mugisha, Paul G Coleman, Susan C Welburn
- Bulletin of mathematical biology
- 2014

We present a mathematical model for the transmission of Trypanosoma brucei rhodesiense by tsetse vectors to a multi-host population. To control tsetse and T. b. rhodesiense, a proportion, ψ, of cattle (one of the hosts considered in the model) is taken to be kept on treatment with insecticides. Analytical expressions are obtained for the basic reproduction… (More)

- Christopher Desmond, Faikah Bruce, +4 authors Alex Welte
- AIDS
- 2014

We outline the benefits, challenges and possible approaches to developing mathematical models that could be used to estimate the magnitude of negative consequences of adult HIV infection for children. Adult HIV infection can lead to numerous negative consequences for dependent children, including depression, anxiety, withdrawal from school and early sexual… (More)

- J W Hargrove, R Ouifki, J E Ameh
- Medical and veterinary entomology
- 2011

Tsetse exhibit a U-shaped age-mortality curve, with high losses after eclosion and a well-marked ageing process, which is particularly dramatic in males. A three-parameter (k(1) -k(3) ) model for age-dependent adult instantaneous mortality rates was constructed using mark-recapture data for the tsetse fly Glossina morsitans morsitans Westwood (Diptera:… (More)

- Carel Pretorius, Nicolas Bacaër, Brian Williams, Robin Wood, Rachid Ouifki
- Clinical infectious diseases : an official…
- 2009

- Rachid Ouifki, Gareth Witten
- Biosystems
- 2009

We consider a model of HIV-1 infection with a reverse transcriptase inhibitor (RTI) therapy and three delays: the first delay is defined as the time from the virus entry into the target cell to the reverse transcriptase step, the second delay represents the time from the virus entry to the production of new viruses and the third delay corresponds to the… (More)