A mathematical model for Crimean-Congo haemorrhagic fever: tick-borne dynamics with conferred host immunity.

Crimean-Congo haemorrhagic fever (CCHF) is a highly contagious tick-borne disease that impacts many countries in parts of Africa, Europe, Asia, and the Middle East. Outbreaks are episodic, but deadly. Due to the highly contagious nature of this disease, suspected cases are taken extremely serious, with very strong control measures implemented almost immediately. It is primarily those living on farms, livestock workers, and medical workers who are at risk. The virus responsible for CCHF is transmitted asymptomatically and transiently to livestock, and symptomatically to humans. The fatality rate in human cases can be very high. The number of methods and directions of viral transmission is large, including tick-to-tick, tick-to-livestock, tick-to-human, livestock-to-tick, livestock-to-human, and human-to-human. We model CCHF using a deterministic system of nonlinear differential equations. This compartment model allows us to analyse threshold parameters and equilibria describing the magnitude and progression of cases of the disease in a hypothetical outbreak.

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.

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.