Assessing the Impact of Vaccination on Controlling the Spread of Human Scabies

Scabies is among the infestations almost forgotten due to its association with poor communities. We formulate a deterministic model to assess the possible impact vaccination will have on scabies control. The Descartes’s rule of signs is used to show the nature of the endemic equilibria. Analysis of the reproduction number and numerical simulations suggest that vaccination in addition to treatment will help greatly in reducing the spread of scabies infestation. This suggests there is a strong need for researchers to come up with a possible vaccine in that order to effectively control scabies especially among the disadvantaged communities. 1. Introduction Scabies is a highly contagious skin infestation caused by skin infestation with the mite Sarcoptes scabiei and is spread by direct contact. Its common name is the “itch mite” derived from the severe pruritis it causes [1]. The female mite burrows the skin and lays its eggs which hatch into larvae within 2-3 days [2]. The larvae then burrow to reach the skin surface, then dig burrows where they pass through two further developmental stages (protonymphs and tritonymphs) before moulting into either male or female mites. As a result a result, S-shaped trails accompanied by small insect bites cover infested areas. It is only less than 1% of the eggs laid by female mites that develop into adult mites [3]. Following infection, the mite population increases rapidly up to 25 adult mites after 50 days and upto 500 mites by 100 days [3], and thereafter rapid decrease may be due to scratching as well as host immune's response. However, 10–12 mites are enough to cause a burden in a host [1]. It is estimated that, despite the availability of effective treatment, over 300 million people in the world are scabies infested [6]. Scabies is well described in the historical record with descriptions evident in ancient texts from China, India and the Middle East [7]. Scabies was also a scourge in London during the First World War upto 1920 [8]. Scabies can be treated with any of the following medications: permethrin (one of the most effective and most expensive), ivermectin (an oral medicine shown in clinical studies to be effective against scabies but not recommended for children), lindane (effective though there are concerns that it can cause neurotoxicity), benzyl benzoate, crotamiton, malathion, and sulphur preparations. Due to low cost, benzyl-benzoate and sulphur ointments are commonly used in developing countries. In general the prevalence of scabies is not well documented especially in Africa [2]. Scabies infestations