Optimal control of intervention strategies and cost effectiveness analysis for a Zika virus model
by: Abdulfatai A. Momoha, Armin Fügenschuh
This paper presents an optimal control strategy and a cost effectiveness analysis for the Zika virus disease. A mathematical model for the transmission of the Zika virus is considered with four preventive measures as control, namely: the use of treated bednets, the use of condoms, a medical treatment of infected persons, and the use of indoor residual spray (IRS). We obtain the reproduction number R0 for the disease and carry out a stability analysis. We observe that the disease’s free equilibrium state is stable when R0 < 1 but unstable when R0 > 1, which leads to a spread of the disease.We examine the implementation of various combinations of the possible control strategies in order to determine the most cost-effective one. Based on the computational results, we conclude that a strategy that consists of treated bednets, treatment of symptomatic infected humans and indoor residual spray is the most cost effective strategy.
Zika is a viral infection that is usually spread by the bite of an infected mosquito. It can sometimes be spread by having sex with an infected human. The Zika virus is a flavivirus and is related to other arboviruses such as the yellow fever virus, the Japanese Encephalitis Virus, the Dengue Virus and the West Nile Virus. In 1947, the Zika virus was originally isolated from a febrile sentinel rhesus monkey and from a pool of Aedes Africanus mosquitoes in the Zika forest in Uganda during a yellow fever study. The Zika virus was first detected in humans five years later in 1952 using neutralizing antibody testing in sera from East Africa, and it was first isolated in a human in Uganda. It has been estimated that about 80% of infected persons with the Zika virus are asymptomatic and it is known that those with clinical manifestations present Dengue-like symptoms that include arthralgia, particularly swelling, mild fever, lymphadonopathy, skin rash, headaches, retro or bital pain and conjunctivitis which normally last for 2–7 days. The epidemic capacity of the Zika virus was revealed in an outbreak in Micronesia in 2007 and affected approximately 5000 people. Zika has been detected in serum, saliva, urine, and semen. It has also been detected in urine and semen even after it disappears from blood. It has also been observed that the Zika virus can be transmitted through sexual contact. It was reported infected that an infected male had infected a female by having vaginal sexual intercourse, even before the onset of symptoms. After the confirmation of the first case of sexually transmitted Zika virus in Dallas County by the CDC on February 2, 2016, six more confirmed and probable cases of a sexual transmission of the Zika virus in the US were reported by the CDC on February 26, 2016, and Europe’s first case of a sexually transmitted Zika virus was diagnosed in France in February 2016. Education about the Zika virus’ mode of transmission and ways of preventing transmission are essential in order to halt mosquito growth and thus Zika spread among a community or population, at regional, national, and global levels. Control measures available are limited and include the use of insect repellents to protect humans against mosquito bites and sex protection while engage in sexual activities. In this paper, we present optimal control strategies and cost effectiveness analysis to better understand ways to control the transmission of the Zika virus with respect to cost/benefit to the population. The paper is organized as follows. In Section 2 we present a mathematical model for the Zika virus transmission with four control functions. In Section 3 we carry out our mathematical analysis of this Zika virus model. In Section 4 we economically assess the control strategies involved in the optimal control problem. In Section 5 we propose an optimal control problem for the minimization of the number of asymptomatic infected humans, symptomatic infected humans and total mosquito population while taking note the cost of control interventions. Finally, in Section 6 the numerical results are analyzed and interpreted from an epidemiological point of view and cost effectiveness analysis was implemented for the various strategies considered in this work.