An eco‐epidemic model for infectious keratoconjunctivitis caused by Mycoplasma conjunctivae in domestic and wild herbivores, with possible vaccination strategies

Abstract

In this paper, we propose an eco‐epidemiological predator–prey model, modeling the spread of infectious keratoconjunctivitis among domestic and wild ungulates, during the summer season, when they intermigle in high mountain pastures. The disease can be treated in the domestic animals, but for the wild herbivores, it leads to blindness, with consequent death. The model shows that the disease can lead infected herbivores or their predators to extinction, even if it does not affect the latter. Boundedness of solutions and equilibria feasibility are obtained. Stability around the different equilibrium points is analyzed through eigenvalues and the Routh–Hurwitz criterion. Simulations are carried out to support the theoretical results. Sensitivity with respect of some parameters is investigated. The prey vaccination as control measure is introduced and simulated, although at present, the vaccine is not yet available, but just being developed. It would then possibly eradicate the infection in the domestic animals, which are considered a disease reservoir. Copyright © 2016 John Wiley & Sons, Ltd.

Predator – Prey/Host – Parasite: A fragile ecoepidemic system under homogeneous infection incidence

“…Also microparasites may infect both the prey and the predator as tuberculosis bacteria in a lion-buffalo system [16] or rabies virus in a rabbit-fox system [66]. A system where the prey (small ruminants) does not pass on the parasite (a mycoplasma) to the predator (golden eagle, red fox) is considered in [1], but here density-dependent incidence is chosen, infected hosts can become susceptible again, and some susceptible hosts are vaccinated. The real world system closest to our model that we could find in the literature [6] has phytoplankton as prey/host, zooplankton as predator and a virus as microparasite.…”

“…h(g(0)/µ) is equivalent to 1 < g(0)/µ. We choose S = K. Then the inequalities take the form µ h (1) < σ < g(0) h(g(0)/µ) , 0 < µ < g(0), µ h (0) < σ < µ + κg K 1 + γ h(1)(1 + κ) ,…”

“…Since h(1) < h(g(0)/µ), we can and do choose some sufficiently large γ > 0 such that g(0) h(g(0)/µ) < g K 1 + γ h (1) .…”

“…To underpin the concern that environmental change of whatever sort (climate, habitat encroachment or fragmentation) can flip an ecosystem from stable persistence to sudden total collapse, we consider a class of so-called ecoepidemic models. Some ecoepidemic models [47] consider several hosts and a parasite that mediates or otherwise influences competition [5,37,41] or cooperation [63] between them; others consider a predator-prey-parasite system where the parasite afflicts the prey or/and the predator and affects the predation process ( [1,2,4,8,9,11,12,16,26,27,39,40,46,48,52,51,64,65,68,69,70,71] and the references therein).…”

“…We will use Theorem A.4 from [60]. Define x(t) = (S(t), I(t), P (t)), and the vector field via system (1) such that x = F (x). By Assumptions 2.1 and 2.2 all functions in the vector field are locally Lipschitz.…”