B. Nannyonga

The dynamics, causes and possible prevention of Hepatitis E outbreaks.

Rapidly spreading infectious diseases are a serious risk to public health. The dynamics and the factors causing outbreaks of these diseases can be better understood using mathematical models, which are fit to data. Here we investigate the dynamics of a Hepatitis E outbreak in the Kitgum region of northern Uganda during 2007 to 2009. First, we use the data to determine that is approximately 2.25 for the outbreak. Secondly, we use a model to estimate that the critical level of latrine and bore hole coverages needed to eradicate the epidemic is at least and respectively. Lastly, we further investigate the relationship between the co-infection factor for malaria and Hepatitis E on the value of for Hepatitis E. Taken together, these results provide us with a better understanding of the dynamics and possible causes of Hepatitis E outbreaks.

Determining parameter distribution in within-host severe P. falciparum malaria

Numerous studies have been carried out on within-host Plasmodium falciparum malaria with varying results. Some studies have suggested over estimation of parasite growth within an infected host while others stated that evolution of parasitaemia seems to be quelled by parasite load. Various mathematical models have been designed to understand the dynamics of evolution of within-host malaria. The basic ingredient in most of the models is that the availability of uninfected red blood cells (RBCs) in which the parasite develops is a limiting factor in the propagation of the parasite population. We hypothesize that in severe malaria, due to parasite quest for survival and rapid multiplication, the vicious malaria parasite is sophisticated and can be absorbed in an already infected RBC and speeds up rapture rate. The study reviews the classical models of blood stage malaria and proposes a new model which incorporates double infection. Analysis of the model and parameter identifiability using Markov chain Monte Carlo (MCMC) are presented. MCMC uses distribution of parameters to study the model behavior instead of single points. Results indicate that most infected RBCs rupture quickly due to the disease instead. This may explain anemia in malaria patients and lack of uniformity of oscillations in within-host malaria. Therefore, more needs to be done as far as within-host malaria is concerned, to provide step by step evolution of malaria within a host.

A mathematical model for the dynamics and MCMC analysis of tomato bacterial wilt disease

In this paper, we formulate and analyze a mathematical model to investigate the transmission dynamics of tomato bacterial wilt disease (TBWD) in Mukono district, Uganda. We derive the basic reproduction number R0 and prove the existence of a disease-free equilibrium point which is globally stable if R0 1. Model parameters are estimated using the Markov Chain Monte Carlo (MCMC) methods and robustness tested. The model parameters were observed to be identifiable. Numerical simulations show that soil solarization and sensitization of farmers can help to eliminate the disease in Uganda. A modified tomato bacterial wilt model with control terms is formulated.

Modelling optimal allocation of resources in the context of an incurable disease

Nodding syndrome has affected and led to the deaths of children between the ages of 5 and 15 in Northern Uganda since 2009. There is no reliable explanation of the disease, and currently the only treatment is through a nutritional programme of vitamins, combined with medication to prevent symptoms. In the absence of a proper medical treatment, we develop a dynamic compartmental model to plan the management of the syndrome and to curb its effects. We use incidence data from 2012 and 2013 from Pader, Lamwo and Kitgum regions of Uganda to parameterize the model. The model is then used to look at how to best plan the nutritional programme in terms of first getting children on to the programme through outreach, and then making sure they remain on the programme, through follow-up. For the current outbreak of nodding disease, we estimate that about half of available resources should be put into outreach. We show how to optimize the balance between outreach and follow-up in this particular example, and provide a general methodology for allocating resources in similar situations. Given the uncertainty of parameter estimates in such situations, we perform a robustness analysis to identify the best investment strategy. Our analysis offers a way of using available data to determine the best investment strategy of controlling nodding syndrome.

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.