Epizootic hemorrhagic disease (EHD) causes varied clinical outcomes across ruminants and geographical locations. Northern white-tailed deer experience infrequent, high-mortality outbreaks; southern white-tailed deer experience seasonal, lower-mortality infections; and African cattle experience endemic, subclinical infections. These observations provide a natural setting to explore how environmental exposure impacts the evolution of host defense strategies. In this paper, we develop a Darwinian pathogen-epidemic model that couples host-pathogen population dynamics with the evolution of resistance (recovery from pathogen) and tolerance (minimizing the effects of infection) traits. We obtain the basic reproduction number $ \mathcal{R}_0 $ and show that the unique disease-free equilibrium is locally asymptotically stable if $ \mathcal{R}_0 < 1 $ and unstable if $ \mathcal{R}_0 > 1 $, consistent with the corresponding purely ecological model. However, we also identify key differences between the models, as the evolution of traits can have a stabilizing effect and may promote bistability. Numerical simulations reveal that high pathogen burden and transmission favor the evolution of tolerance, whereas low pathogen burden promotes the evolution of resistance. Host-intrinsic factors, such as natural death rates and density-dependent suppression of growth, lead to resistance evolution, whereas high host reproductive rates lead to tolerance. Applying our model to EHD shows that intermittent exposure in northern deer leads to no evolved defense, seasonal exposure in southern deer results in the evolution of resistance, and endemic exposure in African cattle selects for tolerance. Furthermore, we demonstrate that continuous vs. periodic control of the disease vector population can lead to the evolution of different defense mechanisms. These findings highlight how environmental and host-pathogen factors shape the evolution of defense strategies, thereby informing disease management and control in wildlife and livestock populations affected by pathogens, such as the EHD virus.
Citation: Anuraag Bukkuri, Sabrina Streipert, Yun Kang. Darwinian dynamics of Host-Pathogen interactions[J]. Mathematical Biosciences and Engineering, 2026, 23(4): 845-883. doi: 10.3934/mbe.2026034
Epizootic hemorrhagic disease (EHD) causes varied clinical outcomes across ruminants and geographical locations. Northern white-tailed deer experience infrequent, high-mortality outbreaks; southern white-tailed deer experience seasonal, lower-mortality infections; and African cattle experience endemic, subclinical infections. These observations provide a natural setting to explore how environmental exposure impacts the evolution of host defense strategies. In this paper, we develop a Darwinian pathogen-epidemic model that couples host-pathogen population dynamics with the evolution of resistance (recovery from pathogen) and tolerance (minimizing the effects of infection) traits. We obtain the basic reproduction number $ \mathcal{R}_0 $ and show that the unique disease-free equilibrium is locally asymptotically stable if $ \mathcal{R}_0 < 1 $ and unstable if $ \mathcal{R}_0 > 1 $, consistent with the corresponding purely ecological model. However, we also identify key differences between the models, as the evolution of traits can have a stabilizing effect and may promote bistability. Numerical simulations reveal that high pathogen burden and transmission favor the evolution of tolerance, whereas low pathogen burden promotes the evolution of resistance. Host-intrinsic factors, such as natural death rates and density-dependent suppression of growth, lead to resistance evolution, whereas high host reproductive rates lead to tolerance. Applying our model to EHD shows that intermittent exposure in northern deer leads to no evolved defense, seasonal exposure in southern deer results in the evolution of resistance, and endemic exposure in African cattle selects for tolerance. Furthermore, we demonstrate that continuous vs. periodic control of the disease vector population can lead to the evolution of different defense mechanisms. These findings highlight how environmental and host-pathogen factors shape the evolution of defense strategies, thereby informing disease management and control in wildlife and livestock populations affected by pathogens, such as the EHD virus.
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Anuraag Bukkuri, Sabrina Streipert, Yun Kang. Darwinian dynamics of Host-Pathogen interactions[J]. Mathematical Biosciences and Engineering, 2026, 23(4): 845-883. doi: 10.3934/mbe.2026034
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