Mathematical models with antibody and cytotoxic T lymphocyte responses due to hantavirus infections in rodents and humans

Viral-hemorrhagic fevers are a suite of diseases that pose a threat to public health. These viruses induce an overwhelming response of cytotoxic T-cells (CTLs) which eliminates the virus by either killing or damaging infected cells. This response may lead to a considerable loss of functioning cells that are critical to the appropriate execution of certain processes. For hantavirus, a zoonotic disease carried by rodents, many of the target cells are the specialized endothelial cells that regulate solute movements, and are hence essential components of osmotic regulation and metabolic waste disposal of particular solutes in the blood. Because of the intimate relationship these endothelial cells have with the vascular system, an infection from the hantavirus may lead to either hantavirus pulmonary syndrome (HPS) or hemorrhagic fever with renal syndrome (HFRS). A crucial loss of too many functioning cells results in pulmonary edema, hemorrhage and even death.

Rodents are the natural reservoirs for hantavirus that spread the virus to humans. Mice have been exposed to this virus much longer than humans and may have co-evolved with the virus. Because of this, rodents have developed a mechanism of down-regulation of their own CTL response. This means that hantavirus infection does not result in fatality in rodents; this is good for the virus as well as the rodents. Humans, having had limited exposure to the virus in evolutionary time, have yet to develop a means of co-existing with hantavirus. When there is no previous exposure to, or memory for, the virus, it is the natural response of our immune system to attack an infection via the CTL response, resulting in many of the symptoms associated with HPS or HFRS.

We use a mathematical model for the virus and the immune response, including antibodies and the CTLs, to describe the cellular dynamics of a viral infection. The original model is an extension of a model originally formulated by Wodarz \cite{wodarz}, a system of ordinary differential equations (ODEs) for healthy target cells, infected target cells, virions, antibodies, and CTLs. Our extension includes T-helper cells which are important in CTL activation and antibody production. In addition, we extend this ODE model to a stochastic differential equation model. It is the aim of these models to predict the effects of the immunological mechanisms on the host both in human and in rodent reservoirs. Understanding the mechanisms by which rodents are able to successfully down-regulate the immunological response to hantavirus will help in finding appropriate treatments for this disease in humans.