A mathematical modelling study of HIV infection in two heterosexual age groups in Kenya.

The control of HIV demands different interventions for different age groups. In the present manuscript, we formulate and analyze a mathematical compartmental models of HIV transmission within and between two age groups in Kenya. We fitted the model to data using MCMC technique and inferred the parameters. We also estimate the reproduction numbers, namely within age group transmission and between age groups transmission basic reproduction numbers. The analysis of the data revealed that there is significant difference in mean number of new HIV infections between males and females within the two age groups. More, particularly, females are highly infected with HIV as compared to their male counterparts. Calculation of the reproduction numbers within and between age groups provides insights into control that cannot be deduced simply from observations on the prevalence of infection. More specifically, the analysis showed that the per capita rate of HIV transmission was highest when there is interaction between young adults to adults and most HIV infections occurred in adult population. Furthermore, the sensitivity analysis demonstrated that the reproduction numbers depend mainly on the probabilities of infection. This results can be used to guide HIV interventions, condom distribution and antiretroviral therapy. Precisely, the results can be used to educate the young adults on practicing safe sex with their partners in order to contain the occurrence of new infections.

An optimal control problem for ovine brucellosis with culling.

A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnseba et al. [A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2-11. Available at http://www.math.u-bordeaux1.fr/∼pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost.

A mathematical model for the dynamics of HIV/AIDS with gradual behaviour change.

An HIV/AIDS model that incorporates gradual behaviour change is formulated with a variable force of infection for the adult population. The variability is modelled using a general function of time since introduction of the initial infective and exemplified for three specific functions. Expressions for the time taken for the reproductive number to reduce to unity and expressions for the time taken to attain a stationary steady state are deduced and discussed. Model projections for urban, peri-urban and rural Uganda are compared with corresponding antenatal clinic sites prevalence trends. The analysis shows that the dramatic decline in HIV prevalence in Uganda in the early 1990s was only possible through drastic declines in the force of infection. Since prevalence was high and reductions in frequency of sexual acts was minimal, the huge reduction could be attributed to reductions in probability of transmission per sexual act probably due to increased selective condom use among high risk sexual partnerships since overall condom use was low.

Mathematical model for HIV/AIDS with complacency in a population with declining prevalence.

An HIV/AIDS model incorporating complacency for the adult population is formulated. Complacency is assumed a function of number of AIDS cases in a community with an inverse relation. A method to find the equilibrium state of the model is given by proving a stated theorem. An example to illustrate use of the theorem is also given. Model analysis and simulations show that complacency resulting from dependence of HIV transmission on number of AIDS cases in a community leads to damped periodic oscillations in the number of infectives with oscillations more marked at lower rates of progression to AIDS. The implications of these results to public health with respect to monitoring the HIV/AIDS epidemic and widespread use of antiretroviral (ARV) drugs is discussed.