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.

Coevolutionary interactions between a haploid species and a diploid species.

We investigate a general model describing coevolutionary interaction between a haploid population and a diploid population, each with two alleles at a single locus. Both species are allowed to evolve, with the fitness of the genotypes of each species assumed to depend linearly on the frequencies of the genotypes of the other species. We explore the resulting outcomes of these interactions, in particular determining the location of equilibria under various conditions. The coevolution here is much more complex than that between two haploid populations and allows for the possibility of two polymorphic equilibria. To allow for further analysis, we construct a semi-symmetric model. The variety of outcomes possible even in this second model provides support for the geographic mosaic theory of coevolution by suggesting the possibility of small local populations coevolving to very different outcomes, leading to a shifting geographic mosaic as neighboring populations interact with each other through migration.