Mathematical Models for Hantavirus Infection in Rodents

Abstract

Hantavirus pulmonary syndrome is an emerging disease of humans that is carried by wild rodents. Humans are usually exposed to the virus through geographically isolated outbreaks. The driving forces behind these outbreaks is poorly understood. Certainly, one key driver of the emergence of these viruses is the virus population dynamics within the rodent population. Two new mathematical models for hantavirus infection in rodents are formulated and studied. The new models include the dynamics of susceptible, exposed, infective, and recovered male and female rodents. The first model is a system of ordinary differential equations while the second model is a system of stochastic differential equations. These new models capture some of the realistic dynamics of the male/female rodent hantavirus interaction: higher seroprevalence in males and variability in seroprevalence levels.

Sex differences in the recognition of and innate antiviral responses to Seoul virus in Norway rats

“…Additionally, the expression of genes that encode for immunological proteins associated with innate antiviral defenses, T cell responsiveness, and antibody production is higher in females than males (Klein et al, 2004a). Mathematical models utilizing ordinary and stochastic differential equations to predict the emergence of hantaviruses reveal that male rodents are more likely to be exposed to hantaviruses and to be infectious following exposure, suggesting that both extrinsic and intrinsic factors are involved (Allen et al, 2006). Production of IFNα/β and downstream expression of IFN-stimulated genes (ISGs) is critical for restricting virus replication and establishing antiviral immunity.…”

Multi-patch deterministic and stochastic models for wildlife diseases

“…Logistic growth has been assumed in models for hantavirus infection in rodents [1,2,[16][17][18] and in many other epidemic models where population growth is limited [19][20][21][22]. In general, the total population size for each patch satisfies the following differential equation:…”

Hanta Virüs Modelinden Elde Edilen Fisher-Kolmogorov Denkleminin Lie Simetri Analizi

“…[3]'de incelenecek olan modelin adi mertebeden diferansiyel denklemler ile verilen durumu, [4]'de Hanta virüs modelinin nümerik çözümleri ile ilgili analizler, [5]'de erkek kemirgenlerdeki Hanta virüs enfeksiyonu için iki yeni model, [6]'da ise Hanta virüs modeli için kesirli mertebeden çalışmalar ortaya konmuştur. [7]'de virüsün tarihsel gelişimi ile ilgili çalışmalar yer almıştır.…”