Search

In this paper, we develop an in-host mathematical model of snakebite envenoming that includes tissue, red blood and platelet cells of humans as specific targets of different kinds of toxins in the snake venom. The model is use to study some harmful effects of cytotoxic and hemotoxic snake venom on their target cells under the influence of snake antivenom. The model has two equilibrium points, namely, trivial and venom free. It has been shown that both the equilibrium points are globally asymptotically stable and numerical simulations illustrate the global asymptotic stability of the venom free equilibrium point. Furthermore, simulations reveal the importance of administering antivenom to avert the possible damage from venom toxins on the target cells. It is also shown through simulation that administering the required dose of antivenom can lead to the elimination of venom toxins within one week. Therefore, we recommend the administration of an adequate dose of antivenom therapy as it helps in deactivating venom toxins faster and consequently enhances the recovery time.

This paper presents a mathematical model with time delay for the transmission dynamics of zoonotic visceral leishmaniasis (ZVL which is caused by protozoan parasite leishmania infantum and transmitted by female sandflies). Qualitative analysis of the ODE version of the model reveals that the disease-free equilibrium of the model is globally asymptotically stable when the basic reproduction number, R0, is less than unity. Using time delay as a bifurcation parameter in the delay-differential version of the model, it has been shown that the incubation period has a significant effect on the stability of the equilibria and we derived the condition for Hopf bifurcation to occur.